m rs - forgotten books
TRANSCRIPT
U NIV E R SITY OFCALIFORNIA .
GIFT OF
M rs . SARAH P . W ALSiW ORTH .
Received October, 1894 .
cflceessions No . 570 (ff) Class No .
UNION R EAD E R,Numb e r O ne .
Iumww n a a u u n
,” u m “ . u m .
UNION R EAD E R, Numb e r Tw o . ANALYSIS OFE NGLISH W ORDS.
UNION SPE AKE R.
SANDERS’
SERIESOFREADERS, &o.Sanders’ Primary Hand Cards. Sanders ’ German and E nglish Primer.Sanders ’
Primary School Charts , Large, for Sanders’ First R eader.the Schoo l Room
,8 Nos. on 4 Cards. Sanders ’
Secon dSanders’ New Speller, D efin er and Analyz er. Sanders’ ThirdSanders’ Test Speller. Sanders’ FourthSanders ’ Old Spelling Book. Sanders ’ FifthSanders ’ Primary Schoo l Primer. Sanders ’ High School Reader.
Sanders’ E locutionary Chart (on Rollers) . Sandcrs ’ Young Ladie s ’Reader
Sanders’ Pictorial Primer. Sanders ’School Speaker.
ROBINSON’
SFULL COURSE OFMATHEMATICS.Graded to the wants of Primary, In termediate , Grammar, Normal and H igh Schoo ls,Academies and
Colleges. This SE rms has already acqui red an An nual sale of n early H A LFAM ILLION, which is rapidly increasmg.
Progre s s ive Tab le B o ok. New Ge ome try and Tri go nome tryProg re s sw e Primary Ari thme t ic . Ro b in so n
’s Ge ome try, s e parat e .
Prog re s s ive Inte lle ctual Ari thme t i c. Ro b in sc n's Trigo nome t ry, s e parate .
Rud ime nts o f W ri tte n Ar i thme t i c. New Analyt i cal Ge ome try and Co n icProg re s s i ve Pract ical Ari thme t i c. Se ct io nsProgre ssw e H i ghe r Arithme t ic. Ne w Surve y i ng and Navigat io n .
Ari thme t i cal E xample s. New D i ffe re nt ial and Inte g ral Calc ulus.Ne w E leme ntary Alge b ra. Ki ddle ' s Ne w E leme ntary Astro nomy.
New U n i ve rs i ty Alge b ra. U n ive rs ity Astro nomy.
Mark ’s First Le sso ns in Ge ome try.
W KEYS to the Arithme tics, Algeb ras, Ge ometries, and Surveying, are published forthe use of Teachers only, an d will b e furn ished at Retail price , po stage paid.ETTHE BE ST.
W E BSTE R ’S UNABR IDGE D
D I C T I O N A R Y
8000 E ngravings ; 1840 Page s Quarto . Price 812.
G. 65 C. M E R RIAM , Publ ishers, Springfield, Mass.
WE BSTE R ’
S SCHOOL D ICTIONAR IE SRichly and profusely ILLUSTRATED
,and embellished with W ood Cuts
,assisting immeasurab ly in the defin i tion of the words under which they occur.
W e b ste r' s Primary Scho o l D i c t io nary. W e b ste r's High Scho o l D ict io nary.
W e b ste r’
s Commo n Sc ho o l D i ct i o nary. W e b ste r' s Academic D i c t i o nary.
M ost valuable TE XT-BOOKS for systemati c in struction in spe lling and pronuncratxon w Scuoons .
W e b st e r's Count i ng -Ho use and Family W e b s te r
’s Po c k e t D ic t i o nary.
D i c t i o nary. W e b ste r's Army and Navy D ic t io nary.
TOWNSEND ’
S ANAL YSIS
CONSTITUTIONOFTHE UNITED STATES.A CHARTo f 52 pages on on e roller
,designed to hang in Class Rooms. An
exposition of the Constitution ; making it one of the most interestingas it is the most importan t study for our youngmen .
TOWNSEND’SANALYSISOFCIVILGOVERNMENT.
A TEXT-BOOKNTO ACCOMPANY THE
CHART OFTH E CONSTITUTION.
W E LLS’
SCIENTIFIC SE RIE S.
CONTAININGTH E
LATEST RESEARCHES IN PHYSICAL SCIENCES,AND THE IR
PRACTICAL APPLICATION TO E VE RY-D AY LIFE .
Scie nce o f Common Things. Principles of Chemistry.
Natural Philo sophy. First Principle s o f Ge o logy.
CRAY’S BOTANICAL SE RIE S
,
By ASA GRAY , Fisher Profe ssor of Natural Science in Harvard Un iversity. Theleading Botanist in America. They have n o equal.
“ H ow Plan ts Grow . Gray’
s Schoo l and Fie ld Book o f
Lessons in B o tany. Bo tany.
M anual Of Bo tany (New E ditiOfl) !Consisting of Gray’s Le sson s
,and Fie ld
,
GrayTs Lessons and M anual in I vo l. Fores t and Garde n Bo tany, b ound ’
m
Gray’
s Field,Forest and Garde n 1 VOL]
Bo tany. M anual,w ith M osses .
Structural and Systematic Bo tany.
BRYANT STRATTON’
SBOOK-KEEPINGSERIES.The be st TEXT-BOOKS ever prepared on this subj ect.
Common Schoo l E dition . H igh Scho o l E ditio n . Coun ting-H ouse E ditio n .
W ILSON’
S SCHOOL HISTORIE SPrimary American H istory. Ame rican H istory, Schoo l E dition .
H isto ry o f the U n ite d States. Outlin es of Gen eral H isto ry.
Parley’
s U n ive rsal H istory.
ROBINSON’
S MATHEMATICAL SERIE S.
AR ITHM ETICAL
E X A M P L E S
TE S T E X E R C I S E S
FOR THE U SE OF
A D V A N C E D C L A S S E S .
N E W Y O R K
SCN3 PE JN N E Y,E L AK E M AN .S
4 7 81. 4 9 GR E E NE STR E E T.
C H I C A G O
1 8 6 9 .
R O B I N S O N ’S
stirs iii i iii ii its,
me most COMPLETE,most PRACTICAL, and most SCIENTIFIC SE RIE S of
MATHEMATICAL TEXT-BOOKS over issued in this country.
R ob in son’s Progre ss ive Tab le B ook ,
R ob in son’s Progre ss ive P rimary A rithme ti c,
R ob inson’s Progre ss iv e In te lle ctual A ri thme tic,
R ob in son’s R udimen ts of W ritten A rithme tic,
R ob inson’s Progre ss ive Practical A ri thme tic,
R ob inson ’s K ey to P ractical A ri thme tic ,
R ob in son’s Progress ive H igher A r ithme tic,
R o b in so n ’s K ey to H igher A r i thme tic ,
R ob in son’s A rithme tical E xample s ,
R ob inson’s New E lemen tary A lgeb ra,
R o b inson’s K ey to E leme n tary A lgeb ra,
R ob in son’s U n ive rs ity Al geb ra,
R ob inson’s K ey to U n iv e rs ity A lgeb ra,
R ob in son’s N ew U n iv ers i ty Algeb ra,
R ob inson’s K ey to N ew U n iv ers ity A lgeb ra,
R ob in son’s N ew Geome try and Trigon ome try ,
R ob inson’s Surv ey ing an d Navigati on ,
R ob in son’s A naly t. Ge ome try an d Coni c Sections ,
R ob in son ’s D ifl’
eren . and In t . Calculus ,
K iddle ’s N ew E leme n tary A s tron omy ,
R o b in son ’s U n ivers ity A stron omy ,
R ob in son’s M athematical Op erat ions ,
R o b in son ’s K ey to Ge ome try an d Trigon ometry , Con ic
Se ctions and Analytical Geometry,
E ntered, according to Act of Congress, in the year 1864, by
D A N I E L W . F I S H , A . H . ,
In the Clerk' s Office of the D istrict Court of the United States, for the NorthernD is trict of New Y ork.
d “J P
r
P R E E'
AC E .
IN the preparation of this work,i t was no t designed to make
a book to take the place of any other, nor one to constitute anece ssary part of the series to which i t belongs, nor to adaptit to the use of beginners
,or those commencing the study of
A rithmetic but it was prepared to meet a demand in gradedand advanced school s for a larger numbe r of carefully prepared and practical example s for review and drill exercise sthan are furnished from ordinary text-books ; and i t may beused in connection w i th any o ther se ries ofArithme tics .Of course
,it is no substitute fo r a systematic treat ise . On
the contrary,i ts leading aim i s to bring toge ther promis
cuously a large number of practical example s, involvingnearlyall the principles and ordinary proce sses of common Arithmetic
,and designed tho roughly to te st the pupil’s j udgment ;
to bring into use his know ledge o f the theory and applicationsof numbers to cultivate a habit of patient investigatio n and
self-rel iance ; to te st the truth and accuracy of his own processes by proo f— the only te st he w ill have to depend uponin all the computations in real bus iness transactions in afte rlife ; in aword, to make him independen t of the text book,and of written rules and analysis .Although the example s are promiscuous
, ye t there i s ageneral classification of them
,the work be ing divided into six
chapters. The first chapter pr! ents the Standards and
iv PR E FACE .
Tables of Weights and Measures ; the second involves theapplications of the Simple Rule s of Arithmetic ; the thirdembraces Common and Decimal Fr actions ; the fourth takesin Compound and Denominate Numbers ; the fifth involvesPercentage
,in all its varied applications and the sixth com
prehends all o ther subjects properly belonging to this science.The example s in each chapte r involve the combination and
appli cation of the principles and processes contained in thepreceding ones
,but not to any exten t those of the fol low ing
chapters . Classes,there fore
,that
,in regular course
,have gone
over the Simple Rules'
of Arithmetic only,w ill find in the
second chapter of this book all they n ee d in the way of supplementary example s for drill and review . Tho se who havefinished
,in any systematic treatise, the study of Fractions,
w ill he re have in chapte r third prope r exerci ses to try the irskill in this part of the science and so they may proceed bysucce ssive reviews
,till the same searching test come s to b e
applied to every part of the subj ect .Two editions are printed one w i th answers at the close o fthe book
,for the use of teachers
,so that when differen t mem
bers o f the same class obtain differen t re sults to the same
example,he may
‘
decide which is co rre ct,w ithout be ing
obliged to take the time nece a ry to so lve or verify it himse lf. The othe r edition i s w ithout answers, and de signedfor the use o f classes.
D . W . F.
NE W YORK,J uly, 1864.
CHAPTE R I.
1. M easure is that by which extent, dimension, capac i ty,or amount is ascertained, determined according to some fixedstandard.
NOTE —The process bywhich the extent, d imension , capacity, or amount is m e t
tained, is called M easurzng and consis ts in comparing the thing to be measured wi thsome conventional standard.Measures are of seven kinds1 . Length. 4 . W eight
,or Force ofGravity.
2 . Surface or Area. 5. Time.’
3 . Solidity or Capacity. 6 . Angles.7. Money or Value.
The first three kinds may be properly divided into twoclas ses—Measures of Extension and Measures of Capac i ty .
MEASURES OF EXTENSION.
2 . E x t ens ion has three dimensions—length,breadth
,and
thickness.A Line has only one dimension length.
A Surface or Area has two dimensions— length and breadth.
I. LINE AR ME ASUR E .
3 . L in ear M easure , also called Long Measure, is usedin measuring lines or distances.
12 inches (in .)3 fe e t5Tyards
,or 16t fee t
,
40 rods8 furlongs, or 3 20 rods,
TABLE .
make 1 foot,
1 yard,
1 rod,
1 furlong,
1 statute mile,
6 M E ASUR E S OF E XTE NSION.
follow ing denominations are also in useused by shoemak ers in
3 barleycorns make 1 Inch,
measuring the length Of
the foo t.
used in measuring the
inches 1 hand he ight of horses directlyover the fore-feet.
1 span,
1 sacred cubit.l pace.
used inmeasuring depthsl fathom, at sea.
0
used inmeasurl .15 statute miles 1 geographicmile
,ing dis tances at
3 geographic l eague.60 of latitude on ameridian
f l‘
t d tbstatute degreeEll
ingtonmgl e on e
3 60 degrees the circumference Of the earth .
Norse —1 . For the purpose ofmeasuring clo th and o ther good s so ld b y the yard ,the yard is divided in to ha lves , f ourths , eighths , and si xteen ths . The Old tab le of
Cloth M easure is prac tically o bso lete .
2. A Span is the d istance that can be reached,Spanned, or measured be tween the
end of the middle finge r and the end of the thumb . Among sailors 8 spans are equalto 1 fathom .
8 . The geographic mile is r}, o f 53-7, or fi fi-fi of the d istance round the center ofthe earth. It is a small fractio n mo re than statute m ile s .
4 . The cub it was o rigi nally the length of a man’s forearm and hand ; or the dis
tance from the e lb ow to the end o f the m iddle finge r5. The length Of a degree o f latitude varie s, be ing m iles at the equato r, 68 9
to mile s in m iddle latitude s , and to miles in the polar regio ns. Them ean or average length, as stated in the tab le , is the standard recen tly adopted bythe U . S. Coas t Survey. A degree of long itude is greate st at the equator, where it ismiles , and it gradually de creas es toward the poles, where it is O.
SURVE YOR ’S LINE AR M E ASUR E .
4 . A Gunter’s Chain, used by land surveyors, is 4 rods,
or 66 feet long,and cons ists of 100 l inks.
TABLE .
inches ( in ) make 1 l ink,
1.
25 links 1 rod,rd.
4 rods,or 66 feet
,1 chain
,ch.
80 chains 1 mile,mi.
NOTE —The denom ination , rods, is seldom used in chain measure, distances b eingtaken in chains and links
M E ASUR E S OF E XTE NSION. 7
II. SQUAR E M E ASUR E .
5. Square M easure i s used in computing areas or surfaces ; as of land, boards, painting, plastering, paving, etc .
TABLE .
144 square inches (sq. in .) make 1 square foot, sq. ft.
9 feet 1 yard,sq . yd.
3 05} yards 1 red,sq. rd .
40 rods l rood,R.
4 roods 1 acre,
640 acres 1 square mile,sq.mi.
Artificers estimate their work as fo llow sBy the square foo t : glazing and stone -cutting.
By the square yard : painting,plastering
,paving
,ceiling
,
and paper-hanginozBy the square Of 100 square feet : flooring
,partition ing
,
roofing,slating
,and tiling.
Bricklaying is ‘ estimated by the thousand bricks,by the
square yard,and by the square of 100 square feet.
NOTE S—1 . In e s timating the painting of moldings , comices, etc , the measuring:line is carried into all the moldings and co rnice s .
2. In e stimating b rick-laying by e ither the square ard or the square of 100 fe e t,the work is understood to b e 12 inche s or i } b ricks t ick.3 .
{Athousand shingles are e stimated to cove r 1 square , be ing laid 5 inches to the
wes t er.
SURVE YORS’SQUAR E M E ASURE .
6 . This measure is used by surveyors in computing thearea or contents Of land.
TABLE .
625 square links (sq. make 1 pole,
P .
16 poles 1 square chain,sq. ch.
10 square chains 1 acre,
A .
640 acre s 1 square mile,sq . mi.
3 6 square miles (6 miles square) 1 township,
Tp.
Non a—l . A square mile of land is also called a secti on .
2 . Canal and railroad engineers commonly use an enginee rs'
chain , which consists
of 100 links , each 1 foo t long.
3 . The con ten ts of land are common ly e stimate d in square m iles , acre s , and hundredths ; the denomination , road, is rapidly going into d i suse .
8 M E ASUR E S OF E XTE NSION.
Ill. CUBIC ME ASURE .
7 . Cub ic M easure , also called Sol id Measure, i s used incomputing the contents Of solids
,or bodies ; as timber, wood,
stone,etc.
TABLE .
cubic inches (cu. in .)cubic feetcubic feet of round timber
,or
hewn
NOTE s .—1. A cub ic yard of earth is called a load .
2 . Railroad and transportation companie s e stimate light freight by the Space itoccupies in cub ic fee t, and heavy freight by we ight.
8. A pile Of wood 8 fee t long, 4 fee t wide, and 4 feet high, contains 1 cord ; and a
cord foot is 1 foot in length of such a pile.
4. A perch of stone or of masonry is 161} feet long, 1; fee t w ide , and 1 foot high.
5. J oiners, b ricklayers , and masons, make an allowance for w indows , doors , etc ,
o f one half the open ings or vacan t space s . Bri cklaye rs and masons,in e stimating
their work by cub ic measure , make no allowance for the corners of the walls of
houses, cellars, e tc , but e stimate the ir work by the girt, that is , the en tire length of
the wall on the outside .
6. E ngineers , in making estimates for excavations and embankments, take thedimen sions w ith a line or measure d ivid ed into fee t and decimals of a foo t. Thecomputation s are made in fe et and decimals, and the results are reduced to cub ic
yards. In civil engineering, the cub ic yard IS the unit to which estimates for ex ca
vations and embankmen ts are finally reduced.7 . In scaling or measuring timb er for shipping o r freighting, gof the solid contents
o f round timb er is deducted for waste in hew ing or sawing. Thus, a log that W i ll.
make 40 fe e t of hewn or sawed timb er, actually con tains 50 cub ic feet by measuremen t ; b ut i ts marke t value is only equal to 40 cub ic fe e t of hewn o r sawed timb e r.H en ce , the cub ic conten ts o f 40 fe e t of round and 50 fe e t of hewn timb er, as e stimated for market, are identical.8 . Sawed timb er, j oists, plank, and scantlings are gene rally bought and sold by
what is called boardmeasure.
9. A cub ic foo t Of water at the maximum density, at the level Of the sea, w eighs
6 25pounds , avoirdupo is.
10. A cub ic foot of lead w e ighs 708? lb s Of b rass , 53 4} lb s of copper, 555l .
o f wrought iron , 486iL lb s . o f cast-i ron , 4501; lb s ; of marb le , 171 lb s : o f grani tc, 165
lb s. of clay,1 3 0 lb s . : of common so il, 124 lb s . ; of b ricks , 194 lb s . of sand , 95lb s
o f sea water, 64—3 lb s Of oak wood , 55lb s . of An thracite re e l
, 54 lb s o f Bituminous coal, 50 lb s of red pine wood, 42 lb s. and of white pine wood, 3 0 lb s.
cubic foo t,
cu. ft.
cubic yard,on . yd .
ton or load,T.
cord foot,
ed. ft.
cord Of wood,Cd.
er h. fp c 0 stoneP011.
ormasonry,
M E A SUR E S OF CAPACITY .1 9
MEASURES OF CAPACITY.
I. LIQUID ME ASUR E .
8 . Liquid M easure , also called Wine M easure, is usedin measuring liquids as liquors, molasses, water, e tc.
TABLE .
4 gills make 1 pint,
pt.2 pints 1 quart
,qt.
4 quarts 1 gallon,
gal .3 14; gallons 1 barre l
, bb l.
2 barrels,or 63 gal. 1 hogshead
,hhd .
Norse —1. The denominations, barrel and hogshead, are used in estimating thecapacity of cisterns, reservoirs , vats , e tc . In Massachuse tts the barrel is e stimatedat 3 2 gallons, in some State s 3 1} gallons, and in others from28 to 3 2 make 1 barrel.2 . The tierce , hogshead, pipe , b utt, and tun are the name s o f casks, and do not ex
pre ss any fixed or defin ite measure s . They are usually gauged , and have the ir
capacitie s in gallons marked on them. Several Of these denominations are still inuse in E ngland.
The follow ing denominations are al so in use9 Old ale gallons make 1 firk in .
4 firk ins 1 barrel Of beer.Imperial gallons 1 firk in .
52—1 lmperial gallons, or1 hogshead.
6 3 wme
70 Imperial 1 puncheon or84 w ine 3
;Of a tun .
2 hogsheads,that is
105 Impe rial gallons or 1 pipe .126 w ine2 pipes l tun .
P ipes of w ine are of different capacitie s,as fo llows
110 w ine gallons make 1 pipe of Made ira.Barcelona
,
1 Vidon ia,or
Teneriffe .
Sherry.
Port.Buce llas, orLisbon .
10 M E ASUR E S OF CAPACITY .
BE E R -M E ASUR E .
9. B e er M easure is a species of liquid measure used inmeasuring beer
,ale
,andmilk .
TABLE .
2 pints (pt ) make 1 quart,
qt.
4 quarts 1 gallon gal .3 6 gallons 1 barrel
,bb l
15barrels, or 54 gallons , l hogshead,hhd.
This measure is no t a standard ; i t i s rapidly falling intodisuse.
II. D RY M E ASUR E .
10 . D ry M easure i s used in measuring articles,no t
l iquid as grain,fruit
,salt
,roots
,ashes
,etc.
TABLE .
2 pints (pt ) make 1 quart, qt.
8 quarts 1 peck,
pk .
4 peek s l bushel,bu . or bush .
The following are sometimes used8 bushels of 70 pounds each make 1 quarter Of wheat .3 6 heaped measure, 1 chaldron of coal .NOTE —The quarter of wheat is 560 pounds, or i of a ton of 2240 pounds.
11 . COMPARATIVE TABLE OFM E ASURE S OF CAPACITY.
Cub ic in . in Cub ic in . in Cub ic in . in Cub ic in . inone gallon . one quart. one pin t. one gill .
W ine measure, 2 3 1 57f 283l 4 1 2Dry measure (2 268 3 67
5 3 3 g 85
NOTE s .—1 . The b eer gallon of 282 inches is re tained in use only by custom.
2 . Grain and some o the r commoditie s are sold by stri cken measure , and in such
cases the measure is to b e s tricken w ith a round s tick or roller, s traight, and of thesame diame ter from end to end.
”
3 . Coal,ashe s , marl, manure , corn in the ear, fruit, and roots are sold by heap
measure. The b ushel, heap measure , is the W inchester b ushel heaped in the formo f a cone , which cone must b e 191} inche s in diameter to the outs ide d iame ter o f
the standard b ushel measure ) , and at least six inches high. A b ushel, heap measure , contains cub ic inche s. or cub ic inches more than a bushel
s tricken measure . Sin ce 1 peck contains cub ic inches, the b ushel,1
heap measure , contains 59 6917 cub ic inches mo re than 5pe ek s. A s this is ab out 1
b u . 1 pk . 12 pt. , it is sufficien tly accurate i n practice , to call 5pe ek s stricken measurea heap b ushel.
4 . A standard bushel, stricken measure , is commonly e stimated at 2150 4 cub ic ih
che s. The old E nglish standard bushel from whi ch the Un i ted States standard bushelwas derived , was kept at W inche ster, E ngland ; hen ce the name.
W E IGHTS. 11
W EIGHTS.
I. TROY W E IGHT.
12 . Troy W e ight i s used in W e ighing gold,silver
,and
j ewels .TABLE .
24 grains (gr.) make 1 pennywe ight, pwt. or dwt.20 pennyweights 1 ounce
, oz .
12 ounces 1 pound,
lb .
NOTE —Troy weight is some times called Goldsmi th’
s Weight.
11. AVOIR D UPOIS W E IGHT.
13 . A vo irdupo is W e ight i s used for all the ordinarypurposes of weighing.
TABLE .
16 drams (dr.) make 1 ounce,
oz.16 ounces 1 pound
,lb .
100 lb . 1 hundred weight,cwt.
20 cwt .,or 2000 lbs. , 1 ton
,T.
NOTE —The long or gross ton ,hundred weight, and quarter were formerly i n com
mon use ; b ut they are now se ldom use d except in e stimating E nglish goods at theUnite d State s Custom-house s, in fre ighting and wholesaling coal from the Pennsyl
vania mines, and in the wholesale iron and plaster trade.
LONG TON TABLE
28 1b . make 1 quarter,
4 qr. 112 lb. 1 hundred weight,
20 cwt. 2240 lb . 1 ton,
The follow ing denominations are also in use8 pounds of butchers’ meat make 1 stone .14 other commodities 1 or gof a cwt.2 stone
,or 28 pounds 1 to dd of wool .
70 pounds of salt 1 bushe l.56 make 1 firk in of butter.100 1 quintal of dried salt fish.100 1 cask of raisins.196 1 barrel of flour.200 1 be ef,p ork, or fish .
280 1 salt at the N.Y . State sal t-wo rks.
12 W E IGHTS;
NOTES—The E nglish quarte r is 28 pounds, the hundred we ight is 112 pounds, andthe ton is 20 hundred we ight, o r 2240 pounds .
2. The we ight of a barrel of flour is 7 quarters of old, o r long ton we ight.
3 . The we ight of a bushel of Ind ian corn and rye , as adopted by most of theState s , and of a bushel of salt is 2 quarters ; and of a barrel of salt 10 quarte rs, o rOf a long ton .
4. The terms gross and net are use d in this we ight. Gross weight is the w e ight o fthe goods, toge ther w ith the b ox , cask, or whatever contains them. Net weight isthe weight of the goods alone .
14 . The weight of the bushel Of certain grains and rootshas been fixed by statute in many o f the States ; and thesestatute weights must gove rn in buying and se ll ing
,unles s
specific agreements to the contrary be made.
TABLE OF AVOIRD UPOIS POUND S IN A BUSHE L,
A s prescribed by statute in the several States named.
35 s
s95 a 2 it;
COMMOD ITIES. g f) 8 E E 233 3 3 s g5: r: w r: 2: Ba: o as q,
M A z 2 2 z z
Barley 48 48 3 2 46 48 48 48Beans 60 60 60
14 14 14
45 50 52 46 42 52 5046 46
60 60 60 60 6425 28
‘
24
3 3 28 3 3
56 56 56 55
H emp Se ed 44 44 44
Ind ian Corn 56 56 56 56 56 53 56 56 56Indian Comm ear.
68
India 1 Corn 50 50 50
M ine rai C OaI* 70 80
28 3 2 3 3 % 3 0 3 2 35 3 0 34 3 2 3 9
Onions 48 57 52 57
Peas
Po tatoe s 60 60 60 60 60
Rye 56 56 56 56 56 56 56Rye M eal 50
SaltT. 50 50 50
Timothy Seed 45 45 45
W heat . 56 60 60 60 60 60 60
W heat B r an 20 20
In Ken tucky 80 lb s. of b ituminous coal, or 70 lb s. of cannel coal, make 1 bushel .
f In Penn sylvan ia 80 lb s. coarse , 70 lb s ground , or 6 2 lb s . fine salt make 1 b ushel ;and in Illino is , 50 lb s . common o r 55lb s. fine salt make 1 b ushel.xIn Maine 64 lb s. of ruta bags. turnips or b e e ts make 1 b ushel.
14 M E ASUR E S OFTIM E AND ANGLE S.
MEASURES OF TIME AND ANGLES.
TIM E .
19. Time is the measure Of duration .
TABLE .
60 seconds (sea) make 1 minute, min .
60 minutes 1 hour,
h.
24 hours 1 day,
da .7 days 1 we ek
, wk .
3 65days 1 common year,yr.
3 66 days 1 leap year,
yr.12 calendar months 1 year
,yr.
100 years 1 century,
The calendar year is divided as fo llowsNO. of month. Season. Names of months. Ab reviations. NO. of days.
J aunar Jan . 3 1W inter. Feb ruaii'y, Feb. 28 or 29
March, Mar. 3 1
Sp ring,
April,
Apr. 3 0
May, 3 1
June,
J un . 3 0
Summe r,
July, 3 1
August,
Aug. 3 1
September,
Sept. 3 0
10 Autumn,
October,
Oct. 3 1
1 1 November,
NOV. 3 0
12 Winter,
December,
D e c. 3 1
NOTE—In most b usiness transactions 3 0 days are called 1 mon th.
M E ASUR E OF ANGLE S.
20 . Circular M easure , or Circular Motion ,i s used prin.
c ipally in surveying, navigation,astronomy
,and geography
,
for reckoning lati tude and longitude , de termining locations Ofplace s and ve sse ls
,and computing difference Of time .
Every circle,great o r small
,i s divisible into the same
number Of equal parts : as quarters,called quadrants ; twelfths,
called signs ; 3 60ths, called degrees, e tc.
TABLE .
60 seconds make 1 minute ,60 minute s 1 degre e , 0
3 0 degre e s 1 sign , S.
12 signs,or 1 circle
,C.
MISCE LLANE OUS M E ASUR ES. 15
NOTES.-1 . M inutes Of the earth
'
s circumference are called geographic or nauticalmiles.2 . A Knot is a nautical or geographical mile . Thus, the expression , ten knots an
hour,” deno te s ten geographical miles per hour.
6086?ne E nglish mile equals 5280 feet, and on e nautical or geographical mile equalsee t.
4. The denomination , sign s, is confin ed exclusively to As tronomy.
5. A degree has no fixed linear exte n t. W hen applied to any ClI‘
Cle it is always
8 3—5 part of the circumference , B ut, strictly speaking, it is not any part of a circle .
6. 90° make a quadran t or right angle ;60° a sex tant or o i a circle.
MISCE LLANE OU S TAB LE S.
2 1. COUNTING.
12 un its or things make 1 dozen.
12 dozen 1 gross.12 gross 1 great gross.20 units 1 score.
23 . BOOKS.
The termsfolio, quarto, octavo, duodecimo , etc., indicate thenumber Of leaves into which a sheet of paper is folded .
A sheet fo lded in 2 leaves i s called a folio .A shee t folded in 4 leaves a quarto
,or 4to .
A sheet fo lded in 8 leaves an octavo,or 8v0 .
A shee t fo lded in 12 leaves a 12mo .
A shee t fo lded in 16 l eave s a 16mo .
A she e t fo lded in 18 leave s an 18mo .
A shee t fo lded in 24 leaves a 24mo .
A sheet folded in 3 2 leaves a 3 2 mo .
24 . COPYING.
72 words make 1 fol io,or shee t Of common law.
90 cc cc 1 cc cc cl' ccChance ry .
16 MONE Y AND CUR R E NCIE S.
MONEY AND CURRENCIES.
1. UNITE D STATE S MONE Y.
25. The currency o f the Un ited ‘States is decimal currency,
and i s sometimes called Federal M oney.
TABLE .
10 mills (m.) make 1 cent, ct.
10 cents 1 dime,d
.
10 dimes 1 dollar, 3 .
10 do llars 1 eagle,E.
COINS°_The gold coins are the doub le ea le ea le b If 1 hdollar pie ce , and dollar.
g g a eag e , quarter eagle, t ree
Thesz lver coins are the half and quarter dollar, dime and half dime , and thre ecent pi ece .
The nickel coin is the cent.
STATE CURR E NCIE S.
26. Un ited States money is reckoned in dollars,dimes
,
cents,and mills
,one do llar being uniformly valued in all
the States at 10 0 cents ; but in many Of the States money issome times reckoned in dollars
,shillings
,and pence.
Georgia Currency.
Georgia,South Carol ina
, 3 1 : 4s . 8d.=56d.
Canada Currency.
Canada,Nova Scotia
, $1 5s. 60d.
New E ngland Currency.
New England States,Indiana
,Illinois
,
M issouri,Virgin ia
,Kentucky
,Ten
h essee,M ississippi
,Texas
,
P ennsylvan ia Currency.
New Jersey, Pennsylvania,Delaware , $1 - '7s 6d z QOdMaryland
,
Ned) York Currency.
New Yo rk,Ohio
,Michigan
,NO
Carol ina. $1 2 88 . 2 96d.
M ONE Y AND CUR R E NCIE S. 17
II. CANAD A MONE Y.
27.The currency of the Canadian provinces is decimal , and
the table and denominations are the same as those Of theUn ited States money.
NOTE —The decimal currency was adopte d by the Canadian Parliamen t in 1858,
and the Act took effect in 1859. Previous to the latter year the mon ey Of Canadawasreckoned in pounds, shillings, and pence , the same as in E ngland .
CoINs .-The silver coins are the shilling
,or 20-cent piece
,
the dime,and half dime.
The copper coin is the cent.I
NOTE s .—The 20-cent piece represents the value of the shilling of the old Canada
currency.
2 . The value of the 20-cent piece in United States mon ey is 183 cents, of the dime3, cents, and of the half dime 4,-3 cen ts.
3 . E very 8d. of the Old coinage is equal to 5cents of the new.
III. ENGLISH MONE Y.
28 . E nglish or Ste rling M oney is the currency of GreatBritain .
TABLE .
4 farthings (far. or qr.) make 1 penny, d.
12 pence 1 shilling,
s.
20 shillings 1 pound or sovereign,or SOV .
NOTE S—1 . Farthings are generally expressedas fractions of a penny ; thus, 1 fan ,some time s called 1 quarte r, (qr. ) id. 3 far. gd .
2 . The gold coins are the sovereign ( z £1) and the half sovere ign
8. The s i lver coins are the crown the half cro'
wn 2s . the shilling,and the 6 penny piece.
4. The capp er coins are the penny, half penny, and farthing.
5. The guinea 218 ) and the half g uinea 105 6d. sterling) are old gold coins,that are sti ll in circulation , b ut are n o longer coined.6. In France accoun ts are kept in francs and decime s. A franc is equal to 18 6
cen ts Uni ted State s money.
7, The pound is not a coin , but stands for 2os . it is repre sen te d b y the sove
re ign , Or the bank no te of 1. The pound is so called , b ecause i ts equivalent, 240d.
or 20s , fo rmerly contained a pound w e ight of siver, the pound then b e ing smalle rthan at present. A po und of standard Si lve r is now co ined into 66s. The value of£ 1 in Canada and the United States Is 854 84. H ence the value of an E ngli sh shillingis cen ts .
18 INTE R E ST.
INTEREST.
29. L egal Intere st is the rate per cent. established bylaw . It varies in different State s, as fo llowsAlabama
,8 per cent. M inneso ta, 7 per cent .
Arkansas,
6 M ississippi, 8
California,
10 Missouri, 6
Connecticut, 6 New Hampshire,6
Delaware,
6 New Jersey, 6
Dist. Of Columbia, 6 New York , 7
Florida,
8 North Carolina,6
Georgia,
7 Ohio, 6
Ill inois,
6 Pennsylvania,
6
Indiana,
6 Rhode Island,
6
Iowa,
6 South Carolina,
7
Kentucky,
6 Tennessee, 6
Louisiana,
5 Texas,
8
M aine,
6 U . State s (debts) , 6M aryland , 6 Vermont
,6
M assachusetts, 6 Virgin ia,
6
M ichigan , 7 W isconsin,
7
NOTE S —l . The legal rate in Canada, Nova Scotia, and Ireland is 6 pe r cent , andin E ngland and France 5per cen t.
2. W hen the rate pe r cen t . is n o t specified In accounts, no te s, mortgages, contracts,e tc.,
the legal rate is always unde rstood.
TABLE .
3 0 . Showing the number of days fromany day of on e mon th
to the same day of any other mon th within one year.
TO TH E SAM E D AY OFTH E N E XT
Jan. Feb . Mar . Apr. May. June J uly. Aug. Sept. Oct. Nov . D ec .
ARITHMETICAL EXAMPLES.
CHAPTE R I I .
1. The total length of railroads in Massachuse tts , Jan . l st,
1864,was 1941 miles, and the total cost of the roads and
equipments tip to the same date, was 366809802 . H owmuch had been expended per mil e ?2 . At the same date there w ere 112 miles Of horse-railroads
,co sting for building and equipments $3 979596 . H ow
much more had be en expended per mile upon horse-railroadsthan upon steam railroads ?3 . A man bequeathed his estate as fo llow s : to each of
his three sons, $8500 ; to each of his four daughters
, $4250
to his w ife, $350 more than the sum of the share s Of one so n
and three daughters ; and the remainde r,which was $2000
more than he gave to all his family,he left to benevolen t in
stitutions . What was the value of his e state 6 3, b
4 . The national debt of Great Britain in 186 1 wasfor each person , and the population was 293 3 4788 .
Whatwas the national debt ?5. At the same date , the annual intere st of the nat ional
debt was 3 12766570 1. Required, the annual in te re s t to eachpe rson .
6 . The Finan ce s of the State Of Maine for the year 18 62
w ere stated as fo llow s
20 ARITIIMETICAL E XAMPLE S.
R eceip ts— Balance in Treasury, Jan . 1
,1862
, 36843 4 63 ;receipts from Taxes
, 343 9150 64 ; rece ipts from Loans andmiscellaneous sources, 32206613 9. E xpenditures
— For warpurpose s
, 3 124088 3 6 ; for so ldiers’ allotments
, 3 109072 3 1
for civil services, 340073 2 45. Required the balance inTreasury
,Jan. 1, 1863 .
7 . The area of Ireland is 3 248 1 square miles, and 5023 984acres are uncultivated. H ow many more acres are cultivatedthan 3 times the number uncultivated
,there being 640 acres
in one square mi le ?8 . In 1861 England paid the United States 3 13 2741 160for cotton ; Egypt, 362253 3 0 ; and India, 3 3 1165565: In 1863she paid the United States 323 02290 ; Egypt, 33 2996465, andIndia
, 3 110258560 . H ow much less was paid for cotton byEngland in 1863 than in 1861 ?9. Western Virginia embraces 51 counties In which there
were , Oct. 1, 1863 , 3 6862 3 whites, 3 981 free colored persons,and 20606 slaves. W hat was the average population in
each county ?10 . During the six months ending March 1
,1864
,1020000
quarters Of wheat w ere e xported from the Un ited State s .H ow many vesse ls
,each carrying 600 short tons
,were re
quired to ship the same11 . The city of New York paid taxes from 1858 to 1864
amounting in the aggregate to 364445967 3 4 . The prOperty upon which these taxes w ere assessed amounted to
353 1194290 in 1858, and 3594196863 in 1863 . HOW muchle ss than the taxe s was the increase Of property ?12 . The number Of pupil s in Girard Co llege in 1857 was
295,and the expen se s f or the ye ar w ere 388173 in 1862 the
pupils numbe red 400,and the expen se s that year w e re
3 7 3 247 . H ow mu ch le ss was the expen se pe r pupil in 1862than in 1857 ?13 . The re w ere in operation
,Jan . 1
,1862
,in the New
22 A RITHM ETICAL E XAMPLE S.
174620 ; Connecticut, 460147. Required the entire populat ion.
2 1 . The Pennsylvan ia Central Railway is 356 mile s long,
and cost 3 3 1450000 the New York Cen tral Railway is 655miles long, and cost 3 3 8825000 ; the Illinois Central is 708mile s long, and cost 3 3 1280000 , and the Mi chigan Central is3 29 miles long and cost 3 14000000. Required the aggregatel ength and cost Of these four roads
.
22 . Of l ibraries contain ing 10000 volumes and upwards,
Massachusetts has 20 , containing an aggregate Of 6 144 15
vols. ; Connecticut 6 , contain ing 1023 73 Rhode Island 3,
contain ing 69868 ; M aine 3 , containing 40700 ; New Hampshire 2 , contain ing 25679, and Ve rmont 1 , contain ing 10000 .
What is the aggregate number of volumes in the se libraries,
and how many more in the l ibrarie s Of Mas sachusetts than inthose Of all Of the other New England States ?23 . In Ill ino i s in 1862 there w ere 98 11 public schools,
which were attended by 519983 scholars. W hat was theaverage number in each school ?24 . A man invests in trade at one time
, 3 680 ; at anothertime
, 3820 ; at a third time, 3 1580 , and on a fourth occasion3420 . H ow much must he add to the sum Of these that theamount may be incre ased three-fold ?25. The Coast Survey i ssued a certain number of hydrographicmaps and charts in 1863
,of which 3 000 were del ivered
to the marine transportation service,4 time s as many 3 00
to the military authorities,and the remainder
,which was 650
le ss than one -half the whole number issued,to the naval
service. What number o f maps and charts were issued ?26 . What number is that which , being divided by 24 , the
quotient increased by 25 1,the sum dimin ished by the dif
ference between 40 and 27,the remainder multipl ied by 4 ,
and the product divided by 11,w ill give 12 for a quotien t ?
27 . France , w ith a population Of 3 6000000 in 186 1 , had anational debt Of per capita. Required her national debt.
A RITHMETICAL E XAMPLE S. 23
28 . The annual inte re s t upon the national debt of Francewas 3 1 10000000 . H ow much was the annual interest to eachperson29. Colorado Territory, organ ized Feb . 28
,1861
,was
formed of 47657000 acre s formerly included in the te rritorie so f Utah and Kansas
,10262400 acre s in that ofNebraska
,and
8960600 acre s fo rme rly in New Mexican te rrito ry . Required,
the numbe r of acre s and square mile s in Co lorado Territory .
3 0 . There were 10869 miles of railway in Great Britain in1862
,the receipts fromwhich w ere 28565355pounds sterling.
Reckon ing a pound sterl ing worth how many dollarswere received per mile ?3 1 . A man worth 3 12750 received a legacy of 3 8000 he
spent 3456 in trave l ing, and gave 3 1000 to a co llege . H ow
much money had he left ?3 2 . The number of 1 and 2 cent internal revenue stampssold in 1863 was 7003 6697
,the value of which was 3 1146
the number of 3 to 20 cent stamps was 23 06502 1,
valued at 3 1520440 18, and of 25 to 40 cent stamps 3 745355,worth 3 100903 9 65. Required
,the number and value of the
stamps of the se denominations .3 3 . Connecticut made
,during the year 1863 , an aggregate
mon thly paymen t of 37063 6 to the familie s o f 83 3 3 soldie rs .
How much was the average amount paid to the family of eachso ldier3 4 . The population of the States in 1860 was 3 1224885,
there being 241 repre se ntatives,how large a repre sem
tation should New York have,whose population was
3 880735?
35. Divide 900 + 2 ) x 5 by (4 x ray- 3 3 .
3 6 . In Ve rmont during the month o f August,1863
,707 1
men were drafted ; 3 583 o f the se w ere exempted,557 failed
to report,145 case s we re undecided and 5 died ; the remain
de r w ere he ld to military service ; of these 183 3 paid com~
24 AR ITHM ETICAL E XAMPLE S.
mutation, and 63 0 furn ished substitutes. H ow many enteredthe service personally ?3 7 . There i s an i sland 40 mile s in circumference. A and
B commence trave ling around it at the same time and place,
but in different dire ctions, A at the rate of 4 miles an hour,
and B, 5miles. H ow far apart w ill they b e at the end of 7
hours ?3 8 . The entire coinage of the U . S. Mint and branche s from
the commencement of their operations til l June 3 0,1863
,was
as fo llows : At Philade lphia,768279944 pieces w ere co ined
,
valued at 350960243 9 14 ; at San Francisco, 1513 6912 pieces,worth 3 1654592882 0 ; at New Orleans
,94890695 pieces
,
w orth 3 7027 1652 13 ; at Charlo tte , 1206954 piece s, w orth3504864150 ; at Dahlonega, 13 8 1750 piece s, w orth 3612 1
and at the Assay Office,New York
,gold and silver
in var ious forms worth 3 13 3 13 15573 5. Required the wholenumber of pieces and the ir value.3 9. A grocer bought 25barre l s o f sugar at 325a barrel ,
and 3 4 barrels at 322 a barre l . H ow much’
would he gainby sell ing the whole at 3 27 a barre l ?40 . What is the area of New England
,there being in
Maine,3 1766 square miles ; in Vermont, 9056 ; in New Hamp
shire,9280 ; in Massachusetts, 7800 in Rhode Island
,1046 ;
and in Connecticut, 47 3 0 ?4 1. The ~ cavalry and artil le ry furn i shed by Illin0 1s up to
Jan . 1, 1863 , amounted to 20916 men,and the cavalry was
12918 more , than the artillery ; the infan try was 985 mo re
than 7 times the cavalry. H ow many men had Ill ino is f urn ished for the war, Jan . 1, 1863
42 .A drover bought cattle for 3 19800, and sold a certain
numb er'
of them for 3 153 60 , at 396 per head , gain ing the reby3960 . H ow much did he gain per head, and how many cattledid he buy ?43 .The exports of flour and wheat from the Un ited State s
to Great Britain were as follows : in 186 1,2561661 barre ls
AR ITHM ETICAL E XAMPLE S. 25
of flour,and 25553 970 bushe ls of wheat ; in 1862
,2672515
barre ls,and 25754709 bushe ls ; in 1863 , 1479413 barre ls, and
‘
23 107 190 bushels. How many more bushe ls of wheat thanbarre ls of flour w ere exported in the thre e years ?44 . Bought 600 bushe ls of po tatoes for 3540 , and sold 3 60
bushels at per bushe l, and the remainder at co st. H ow
much was gained by the transaction ?45. In 1862 Ohio sowed 693 74 acre s of barley, fromwhich
763 114 bushels w ere produced ; 2266129 acre s of corn w ereplanted
,which yie lded 74782257 bushe ls . H owmuch greater
was the yield of corn than barley per acre ?46. Jan . 1
,1863 , there w ere 507 banks in the Eastern
State s,491 in the Middle States
,167 in the Southe rn State s
,
3 07 in the We stern States. H ow many more banks in theEastern and M iddle States than in the Southern and WesternState s ?47 . The sum of the killed and prisoners in the Un ion armyat the battle of Stone River was 3 496
,and the prisoners were
548 mo re than the killed. The w ounded w e re 747 more
than three time s the prisoners. The who le Un ion force eu
gaged be ing 43500, how many were left for duty after thebattle ?48. In 1864 there were 2 3 71members of Congre ss
,and the
salary o f each member was 3 3 000 . H ow much did they allrece ive49. The United States contain an area of 28 198 11 square
miles, and in 1860 there w ere 1 1 inhabitants to the squaremile. What was the entire population50. The New England State s have 35 l ibraries
,contain ing
863 03 5vols. the M iddle State s,28
,contain ing 763 73 3 ; the
Southern States, 24, contain ing 503563,and the We stern
States, 17, contain ing 273 109. What is the average numberof vo lume s in these l ibrar ie s51. A mechan ic earns 375 a month
,but his n ece ssary ex
2
26 A R ITHM ETICAL E XAMPLE S.
penses are 350 per month. H ow long w ill it take him to payfor a farm of 60 acre s wo rth 340 an acre ?52 . A groce r w ishe s to put 1280 pounds of tea in 4 kinds
of boxe s,con tain ing re spe ctive ly 7
,9,10 and 14 pounds
,using
the same number o f bo xes of each kind. H ow many boxe scan he fi ll53 . In 1860 there w e re made in the United State s 1860000gal lons of w ine
,valued at per gallon . H ow many
schoo l houses, worth 3 7
50 each,could be buil t w ith the pro
ce eds
54 . The United States paid 3 6 1000 fo r the site of the Cus
tomHouse at Richmond,Va.
,and contracted for the building
fo r 3 110000 ; the to tal expense to the Government June 1,
1861,was 32520 16 . H ow much did the cost exceed the
price agreed upon ?55. The popul ation of New Orleans in 1850 was 1 163 75;
in 1855,13 9190
,and in 1860
,168675. H ow much more
was the increase in the last five years than in the previousfive years56. In 1861 the importation of specie into the United States
was 3463 3 96 11 , and the expo rtation 3 2979 1080 . What wasthe excess o f impo rtation ove r expo rtatio n57 . 3 16415052 specie was imported in 1862 ,
and 3 3 6886956
was expo rted . H ow much more was the excess o f exportation in 1862 than the e xce ss of importation in 186158. In 1863
, 39555648 specie was imported , and 3 641566 10was exported. W hat was the e xeess of exporta’tio‘
n over importation for the three years ?59. In 1862 there were sent out from the D ead
'
Le tter Officefor de l ivery 10475 l etters, contain ing 34653 8 90 ; of these8766
,contain ing 34 1068 48 were de l ivered, 1593 , containing
3509574 were re turned to the office , and guerillas appropriated the remainder. W hat was the average amount in eachletter lost
AR ITHMETICAL E XAMPLE S. 27
60 . Gunpowder was invented in the year 13 3 0 . Iron was
discovered B . C. 1406. What period of time elapsed betweenthese two events61 . Ofthe appropriation for the CustomHouse in Galve ston
,
3 1640 18 was unexpended, 3 6000 was paid for the site,and
the building co st 3 17850 75mo re than the contracted price,
which was 390509 07 . What was the appropriation ?6 2. M. Smith re nted a sugar orchard con taining 1500
tre e s,agre e ing to assume all the nece ssary expense s in making
sugar,for one -half the quantity made he made on an average
3 % lbs . to e ach tree,and so ld his part of the first 3 000 lbs.
made fo r 25 cents a pound,and the remainde r at 20 cents ;
he paid 360 for labor, 3 3 0 for team work
,and burned 25
co rds of wood worth 32 a cord . H ow much was his gain ?63 . A horse dealer gave 38448 fo r a certain number ofhorses ; he sold a part of them for 37650 at 390 each
,and by
s0'
do ing lost 36 a head .For how much must he se ll the re
mainde r pe r head to gain 3252 on the whole64 . The expenditures of the Po st Office Department in
1860 were 3 1487477 and the gro ss revenueH ow much greate r than the revenue were the expenditures ?65. In 1861 the expense s of the Post Office Department
we re 3 13 60673 9 1 1, and,
the gro ss revenue, 39049296 40.
H ow much more had the expenditures decreased than therevenue from the previous year ?66. In 1862 the expenditure s w ere 3 111253 64 13 , and the
revenue 390 12549 56 . H ow much nearer self-supporting wasthe Po st Office Departmen t in 1862 than in 186167 . In Massachuse tts 3 2079 men were drafted in 1863 ; ofthe se 223 43 w ere exempted
,3 046 failed to report
,and the
remainde r w ere held for service ; of these 743 served personally
,23 25furn ished substitute s, and the remainder paid 3 3 00 .
H ow much commutation money did the Governmen t rece ive ?68 . Jan . 1
,1863
,Rhode Island had furn ished 3 147 men for
28 AR ITHM ETICAL E XAMPLE S.
three mon ths,2069 for n ine months
,and9410 for three years ;
during the year 1863,1246 men were obtained by draft
,7 16
recruits w ere sent to regiments in the field,and two new regi
ments were formed,con tain ing 1800 men ; 425 enl iste d in
other States,and 1400 w ere in the navy. What was the
aggregate number of men furn ished by Rhode Island fo r thewar up to Jan . 1
,1864 ?
69. What must the number be which divided by 453,wul
give the quo tient 3 07,and the remainder 109 ?
70 . A has 3 3 10 ; B, 3558, and C, 3744, w ith which theyagree to purchase ho rse s at the highe st price per head thatw il l allow each man to invest all his money. H ow manyho rses can each man buy7 1 . Of 3 003 cases admitted into the retreat fo r the insaneat Hartford
,Connecticut
,574 were married male s
,and 728
w ere single,704 were married female s, and 73 0 single ; the
remainder w ere w idowed ; the whole number of female s exceeded the whole number of males by 279. Required thenumber of w idow ed male s and females.72 . The rece ipts of the U. S. Tre asury for 1863 w ere asfo llows : Customs
, 3 69059642 ; Public Lands, 3 1676 17 ;
Direct Tax, 3 1485104 ; Internal Revenue , 3 3 7640788 ; Mi s
cellaneous, 3 3 046615; Loans, 37766823 62 . Required the
total rece ipts.73 . The expenditures fo r the same period were as follow sCivil List
, 3 6350618 78 ; Foreign Intercourse, 3 123 14 13 06 ;M isce l laneous
, 3 1567 1890 24 ; Interior Departmen t, 3 42 16520 79 ; War D epartment
, 3599298600 83 ; Navy , 3 63 2 1 1on accoun t o f Public Debt
, 3205816482 . Requiredthe aggregate expenditure s.74 . The balance in the Treasury at the beginn ing of theyear was 3 13 043547 . What was the balance at the end ofthe year
,the receipts and expenses be ing as is stated in the
preceding examples ?75.The State of De laware received 3 603 8551 for general
3 0 AR ITHMETICAL E XAMPLE S.
83 . The sum of two numbe rs i s 2487,and the greater is
553 more than the less . W hat are the numbe rs ?84. The Internal Revenue col le cted for the year endingJune 3 0
,1863
,was 340993 954 97 . The to tal re ce ipts to
Aug . 3 1,1863
,w ere 347489473 03 ; to Sept. 3 0 , 353 625678 .
46 . H ow much le ss was received in September,than in July
and August ?85. A cistern contain ing 1260 gallons has two pipes. By
the first 48 gallons run in to the ciste rn every half hour,and
by the second 3 6 gallons run out in an hour. In how manyhours w ill the ciste rn b e filled ?86 . A man sold 600 bushe ls of wheat at a bushe l
,
and to ok his pay in sugar at 12 cents a pound he afterwardsold one -half his sugar. H ow much had he l eft ?87 . The number of men sen t by Vermont to the war wasas follows : One regiment of 3 -months men
,numbering 782
5 regiments of 9-months troops,contain ing 483 3 men ; one
regiment of cavalry,966 strong ; 2 batte rie s, contain ing 286
men ; 3 compan ie s of sharpshgo ters , averaging 100 men
each ; 10 regiments of 3 -years men ; and 2740 recruits forregiments in the field mak ing the total numbe r of men furn ished for the war
,up to Oct. 1st
,1863
,19607 . What was
the average strength of the 3 -years regiments ?88 . The quota of Vermont under the first call for 500000
3 -years volunteers was 8950 ; under the second call for 3 000003 -years volunteers
,4898
,and the same under the call for
3 00000 95months volunteers. To meet the first two requisitions the State furn ished 13 992 men
,and under the last call
483 4 9-months men . H ow much in exce ss o f her quota wasVermont
,4 9-monthsmen be ing equivalent to 1 3 -years man
89. From 3 40 (20— 4) x (8 + 2) take 3 6—2—3 (28 x 6)
(19
90. A tailor made 2804 pairs of pants in four succe ssiveyears
,making each year 50 pairs more than during the pre
V ious year. H ow many pairs did he make each year ?
AR ITHM ETICAL E XAMPL ES. 3 1
91 . The expenditure s for educational purpo ses in New Yo rkfo r the year 186 1, we re 3 3 842270 8 1 in New Jersey
, 3540
2 83 80 ; in Pe nnsylvania, 3 2
3
893 83 60,and in De laware
,
3 853 3 3 03 H ow much mo re was expended in New Yorkthan in the o the r thre e State s ?92 . The State debt o f Maine at the outbreak of the rebe ll ion stood as fo llows : Debt incurred during the Aroo stookwar
, 3449000 ; debt due Massachuse tts for lands, 3 250000The war debt fo r 1861 was 3 800000 ; during 1862 , 327000 o f
this debt was paid,and there was added to the war debt in
1863, 3950000 What was the total debt of the State
,J an. 1
,
1863,and Jan . 1
,1864 ?
93 . H ow many pounds of sugar at 20 cents per pound ,must b e given for 5 pieces o f co tton clo th
,contain ing 44
yards each , at 42 cents a yard ?94 . A man bo ught 750 acre s of land at 3 20 per acre ; he
so ld at one t ime 3 25 acre s at 32 3 pe r acre , at anothe r time260 acre s at 3 25per acre . At what price per acre must hese ll the remainde r to gain on his purchase 3 194595. According to the census of 1860
,the re were in the
United State s 13 8694 3 4 white male s and 13 13 3 890 female s ;2 3 4000 fre e colo red male s and 253 996 free co lored female s ;1982625male slave s
,and 197 1135 female slave s. H ow
many more male s than female s in the Un ited State s ?96 . 250 x 6—2 x (8 how
many ?97 . In 1860 New Je rs ey cultivated 103 9086 acre s
,worth
3 18028 142 1 ; Maryland cultivated the same year 183 3 3 06
acre s,wo rth 3 145976990 25. H ow much w ere the farms o f
New Je rsey wo rth per acre more than those o f Maryland ?98 . Divide 16 x 72 x 45x 2 1 by 27 x 3 2 x 12 x 3 5.
99. The rebe l army in the battle of Stone River lo st onefourth of all i ts force s engaged ; 3 500 w ere taken prisone rs,and four t ime s this numbe r was 2000 mo re than the killed andw ounded . Required the Confederate force in the battle .
3 2 AR ITHM ETICAL E XAMPLE S.
100. Bought 60 yards of clo th at the rate of 2 yards for35, and 80 yards more at the rate of 4 yards for 39 ; I immediately so ld the whole at the rate of 5yards for 3 14 ; howmuch did I gain10 1 . The quota of New Jersey under the various calls for
troops was as fo llows : l st requi sition,3 123 ; 2d, 3 13 8 ; 3 d,
523 0 ; 4 th, 523 0 ; and 5th, (drafted militia,) 10478 .Unde r
the first call she furn ished 3 105men ; 2d, 3 120 ; 3 d,4th
,4644 ; 5th, 107 14 , and 103 0 recruits for old regiments
in the fie ld w ere enl isted . H ow much in exce ss o f her quotawas New Jersey
,Jan . 1, 1863 ?
102 . Connecticut cultivated in 1862,183 0800 acres
,laid
out in 22885 farms, the to tal value o f which was 3 91540000 .
What was the average value of each farm? Average num
ber of acre s in each farm103 . A farme r exchanged 40 bushels of corn and oats
,
mixed in equal quantities, at and per bushe lrespective ly
,
‘ for wheat and rye in equal quantitie s , atand per bushel respectively . H ow many bushe l s ofwheat and rye did he obtain ?104 . Arkansas Post surrendered to Gen . M cClcrnand
,J an .
11,1863 . The rebe l lo ss in killed and wounde d was 550
,
which was tw i ce the Union lo ss, and the number o f prisonerswas 23 0 less than 6 time s the loss in killed and wounded of
both armies. What was the number o f prisoners ?105. A farmer bought an equal number of horses
,sheep
and hogs for 3 9600 . H e gave 3 108 , 39 and 3 11 per head fo rthemrespectively . What was the number of an imals bought106. The population of t he five l arge st citie s in England in
1861 was as fo llow s London,2803 03 4 ; Liverpool , 443 874 ;
Manche ster,3 3 83 46 ; Birmingham,
295955 Leeds,207 153 .
H ow many more inhabitants in London than in the four othercitie s107. A and B inve sted 3 120 in lottery tickets, A paying 3 3
as often as B 35. C and D invested an equal sum,C paying
ARITHM ETICAL E XAMPLE S. 3 3
34 as often as D paid 36 . They purchased tickets toge theragree ing to share the prizes in proportion to the sums investedby each. The prize s amounted to 37200 . H ow much oughteach to rece ive ?108 . The aggregate rece ipts o f the Post Office Depart
ment for 1863 were 3 1 1163 78959, while the expendi turesduring the same time were 3 113 14206 84. What was thene t expense ?109. A company in a fort numbe ring 75 men have provisions fo r 3 0 days. How many men must depart
,that the
same may last the remainder 45 days ?110 . The rebe l lo ss at Ge ttysburg was reported 40 12 1 ;
the prisone rs w ere 3 7 1 more than half the lo ss in k illedand wounded
,and 4 time s the killed was 1000 mo re than the
wounded . What were the re spective losse s in killed,wounded
and prisoners ?111 . A merchant expended for clo th 37850 . H e so ld a
certain number of yards for 35580 , at 3 15 per yard, andgained on those so ld 3 1860 . H ow many yards did he buy atfirst
,and how much did he gain per yard on the clo th so ld
112 . A horse worth 3 120 , and 4 cows at 328 each,were
exchanged for 3 1 sheep and 346 ‘
in money. What were the
sheep valued at per head1 13 . The quotient of one number divided by ano ther is
74,the diw so r is 3 2 1
,and the remainder 95. What is the
dividend1 14 . The mails of the Un ited State s in 1862 w e re carried
200 1500 mile s by steamboat, at an expense o f 3 3 00225 bycoache s 7268400 mile s, for 3 17444 16 , and by railroad200
,for which 3 2505492 w ere paid . H ow much was the
rate per mile by each mode of transportation ?1 15.
General Meade reported the lo sse s of the Un ion armyat Ge ttysburg 23 186 . The number killed was 290 more
than one -e ighth of the sum of the lo sse s in prisone rs and
gac
3 4 AR ITHMETICAL E XAMPLE S.
wounded, and tw ice the prisone rs was 42 3 le ss than the
wounded . H ow many were the killed,wounded and pri s
oners ?1 16 . Bought 17 cw t. of prunes at 3 15 per cw t.
,and gave
in exchange for them 250 lbs. o f butter at 25 cents pe rpound
,48 dozen eggs at 15 cents per dozen ,
and the remainde r in salt at per bushel . H ow many bushe l s of saltwere required ?1 17 . The population of the seven large s t citie s in France
in 186 1 was as fo llows : Paris,1696 14 1 Lyons
,3 18803 ;
Marseilles, 260910 ; Bo rdeaux , 162750 ; L ille,13 1827 ;
Nante s, 112625 Toulouse,1 13 229. H ow much did the
population of Paris exceed that o f the othe r six citie s ?1 18 . What i s the value o f 16 x 3 125 x 7) (125x
27) x 3 2 )+ 43 264— 16 x 9 ?
1 19 . A trade r purchased a lo t o f ho rses and oxen for
32000 , paying tw ice as much fo r a ho rse as for an ox . Therewere thre e time s as many oxen as horse s
,and the horseSco st
him 380 a head . Required the number o f each .
120 . Required the area of North Ame rica,if the Uni ted
State s contain 2988892 square mile s ; Bri tish Ame rica,
29143 18 ; Dan ish Ame rica , 800000 ; Russian America,3 94
000 ; Mexico,645822 ; and Ce ntral Ame rica
,2 19000 .
12 1. S. J. Eaton bought 75 hhds . mo lasse s at 3 18 per
hhd . H ow much must he charge per hhd. to gain 3 3 00, andwhat w ill be the gain on each ?122 . What were the respective lo sses in the Un ion army
in the battle o f Chickamauga,3 time s the killed be ing 13 le ss
than '
the miss ing, and tw ice the mi ssing be ing 628 more thanthe wounded, and the whole loss 15851123 . If the Pre sident of the Un ited State s expends daily
3 60 , how much w ill he be able to save at the end o f fouryears
,his salary be ing 325000 per annum?
124 . The army pension roll s stood as follows, J uue 3 0,
AR ITHM ETICAL E XAMPL E S. 35
1863 Invalid pensio ners 7248 , to whom 3570648 was payable annually ; Revo lutionary so ldiers, 18, to whom 3 1045
was payable w idows o f Revo lutio nary so ldiers, 1573 , amo untpayable to them 3 129684 ; w idows, mo thers, sisters and
orphans,in wars since the Revo lution , 4820 , annual payment
to the same 3526266 . What was the whole number of pen
s ioners and the sum paid them ?125. I exchanged 5barre ls of vinegar
,e ach contain ing 3 2
gallons,at 25 cents a gallon
,for 5 piece s o f shee ting
,each
contain ing 40 yards. H ow much did i t co st me pe r yard ?126 . In 1860 Virgin ia con tained 19578964 acres o f im
proved laud,w orth 3 3 7 160873 6 72 ; Pennsylvan ia, 6548847
acre s,worth 3 662022943 23 . H ow much mo re w ere the
farms w o rth per acre in the latter State than in the former ?127 . Required the actual value o f my farm if 3 253 44 i s 6
t ime s the sum I paid for it,and i t cost me 3776 less than its
real value.128 . According to the census o f 1860, 20875 o f the popu
latio n o f New Yo rk city w e re born in the Easte rn State s,
3 97980 in the M iddle State s,194 1 in the W e stern State s
,
488 1 in the Border State s,1353 in the Seaboard Slave State s
,
882 in the Southw e st Slave State s,and 2 13 0 in the territo
ries. H ow many of the inhabitants of the city were native sof the Uni ted States129. The fore ign born in New York city in 1860 w ere as
fo llow s : native s o f Germany,1 19984 ; of Great Britain, 244
826 ; o f Conti nental Europe,17235
,and o f various other
countr ies 1672 . Required the to tal fo re ign bo rn .
13 0 . The population o f the city was 629904 in 1855. H ow
much was the increase in 5 years,the population in 1860
be ing as stated in E xample s 128 and 129 ?13 1. Ten men agre ed to gather 1000 bushel s o f cranberrie s
,
and to rece ive fo r their labor one -half the quanti ty gathe red.
Afte r 400 bushe ls w ere gathered 4Wmen w ithdrew,leaving the
3 6 A RI'
I‘
IIM ETICAL E XAM PL E S.
others to complete the job . H ow many bushe ls should eachman receive ?13 2 . F. Harriman purchased 3 18 acres of w ild land fo r
3 6996, and so ld 253 acres at 3 17 per acre , and the remainderat cost. Did he gain o r lose
,and how much ?
13 3 . During the y ear 1863 32876983 was paid to postmasters
,and 3 6541580 for mail transportation . The expen
diture s be ing 3 150417 in excess of the revenue,which was
3 11163 789. How much was expended for miscellaneouspurposes ?13 4 . Havmg money to invest I buy 2 farms worth 34550
each,20 shares ra i lroad sto ck at 3 106 per share , and have
3 250 le ft. H ow much had I at first ?135. The navy pension rolls for 1863 showed that 545navy
inval ids w ere paid 3 3 50 19 ; 577 w idows or children w erepaid 3 107886 , and 10 privateer pensioners w ere paid 3 622 .
H ow many pensioners we re there , and what was the amountpaid13 6 . H ow many barre l s of apples at 34 per barre l must
be given in exchange for 10 bags of wheat, each contain ing 3bushels at 32 per bushel13 7 . During the first three months of 1864 there were 27
gold mining compan ies organ ized in New York city,w ith an
average capital of 3 2 350000 ; 4 silver compan ie s, w ith an
average capital of 3 3 625000 8 coal and iron compan ies,
whose average capital was 3 1250000, and 4 coppe r compan ie s,w ith an average capital of 3 625000 . H ow much capital wasinve sted in min ing compan ies during the thre e months ?
13 8 . What is the number of subje cts belonging to the
Russian Government,there be ing 66891493 in Europe, 8203
197 in Asia,and 54000 in America ?
13 9 . H ow many sheep at must be given in e xchangefor 58 cows at 340 each ?140 . The first se ttlemen t in the Un ite d State s was made
3 8 AR ITHM ETICAL E XAMPLE S.
the ports o f Russia ; 1073 9 vesse l s, tonnage 1026794, departedfrom the same ports. What was the average tonnage of thevesse ls150 . If 850 men require 25500 rations of bread fo r a
mon th,how many rations w ill a garrison of“1250 men re
quire for the same time ?151 . In the month of Sept. 1863
,on account of the Indian
massacre,6588 fugitives fled from the St. Pe ters district in
M innesota,one -n inth as many from the M inneapolis district,
and in other districts 127 mo re than fromM inneapolis . H ow
many were made homeless by this massacre ?152 . From Jan . 1, to April 15, 1864, 27 gold min ing
companie s w ere organized in New York w ith an aggregatecapital of 3 63 450000 . What was the average capital of eachcompany153 . Two persons
,starting from the same place and travel
ing in Oppo s ite directions,are 20 mile s apart at the end of
one hour,but traveling in the same dire ction they are 6 miles
apart at the end of an hour. H ow far does each travel perhour ?154 . The population of France in 1861 was 3 747273 2 ; of
Algeria,2999124 ; and of French colon ies, 3 0623 89. H ow
many subj ects had the French government ?155. Thre e men rented a farm and raised 960 bushels of
grain,which was divided in proportion to the rent paid by
each ; the first was to have on e-half of the whole , the secondtw o -thirds o f the remainde r
,and the third what was left.
H ow much did each receive,the grain being worth 32 a
bushe l ?156 . During the year ending July 1 , 1862 , 9763 le tters
contain ing papers of value o ther than money,were sen t to the
dead letter office,and the follow ing reasons were assigned for
the ir non -de l ivery : He ld for postage,1050 ; misdirected,
1466 mails suspended,3 26 ; refused, 26 ; name of post
AR ITHM ETICAL E XAMPLE S. 3 9
office omitted,86 ; person addressed dead, 27 ; and the o thers
w ere uncalled for. H ow many of this last number w erethere ?157 . Gen . Grant reported the lo sses of the Un ion army in
the serie s of battle s conne cted w ith the taking of Vicksburgas follows : Port Gibson
,13 0 killed
,7 18 w ounded
,and 5
missing ; Raymond,73 killed
,3 65wounded
,and 3 2 missing ;
Jackson,40 killed
,24 0 w ounded
,6 mi ssmg ; Champion ’s
Hill,426 killed
,1842 wounded
,189 missing ; Big Black
Bridge,29 killed
,242 w ounded
,2 missing
,and the lo sses
befo re Vicksburg made the entire loss 8875. This was so
distr ibuted that the to tal missing were 706 le ss than thek illed
,and the wounded were 25 less than 4 times the sum
of the k illed andmissing. Required the number of killed,wounded andmissing before Vicksburg.
158 . The forward whe els o f a carriage are 7 fee t in circumference
,and the hind wheel s 10 . H ow many time s w i ll each
revolve in passing over 42 mi le s,there be ing 5280 fe e t in a
mile159. A man paid 3 1024 fo r a farm, 3250 fo r drainage , 350
f or fencing,and for hired labor
, 3 3 76 . The gro ss proceeds o fone year amounted to 32 100 ; w ith the profits he purchasedan equal number of sheep at 3 3 each, and horse s at 377 apiece. H ow many of each did he buy ?160 . The population of Great Britain and Ireland in 1863
was estimated at 3 0000000 , and the value of real and personal property
, 3 3 3 402600000 at the same time the e stimatedpopulation of the loyal State s was 24000000, and the valueo f property
, 3 13 929840000 . H ow much more property toeach pe rson in the United Kingdom than in the loyal States161 . The products o f Great Britain and Ireland in 1863 ,
amounted to 3 3 3 40200000 , and in the Loyal States to 3 3 720000000 . H ow much more was the value of the annual products to each person in the loyal States than in Great Britainand I reland ?
40 Anz'
rHM ETICAL E XAMPLE S.
162 . Suppose two locomo tives start from the same placeand move in the same direction
,the first at the rate of 3 0
mile s an hour,and the Second 20 mile s ; afte r the first has
gone 150 mi le s i t commences a backward movement w ith thesame ve locity till i t mee ts the second englue . H ow far fromthe point of starting, and in how many hours do they mee t ?163 . The Internal Revenue co lle cted upon advertisements
in 1863,at the rate o f 3 cents upon a do llar
,amounted to
340629. What was paid for adverti s ing during the year ?164 . What number is that which be ing divided by 72
,the
quo tient increased by 25,the sum dimin ished by the differ
ence be tw e en 25and 18,the remainder multiplied by 7
,and
the product increased by (9 x 8) (3 x 4) the sumw ill b e 167 ?165. In D ec . 1862 , the Un i ted State s Navy numbe red 427
vesse ls,carrying 3 268 guns
,tonnage 3 4003 6 ; in D ec.
,1863
,
the re w ere 588 ve sse ls, carrying 4443 guns , to nnage,467967 .
What was the increase in vessel s, guns and tonnage ?166 . H ow many subj ects are claimed by the British
governmen t,there be ing 29458442 in Europe
,449674 1 in
Ame rica,1020525 in Africa, 173 73 8866 in Asia, and 3 423
996 in Australia ?167 . In 1862 New Hampshire reported 2352 schoo l dis
tricts,and 84672 children who attended scho o l . Requ i red
the ave rage attendance in each district.168. Bought 25 sheep for 356 ; how much less per head
should I have paid , had I purchased 7 more she ep w ith thesame money169. According to the census of 1860, the population of
Maine was 628279 ; New Hampshire,3 26073 ; Ve rmont,
3 15098 ; Massachuse tts, 123 1066 ; Connecticut, 460147
Rhode Island,174620 ; New York
,3 88073 5. H ow many
more inhabitants in New York than in New England ?170 . A and B pay fo r a barrel of apple s, and 20
cents for the barrel A contributes and BA
the remaino
AR ITHM ETICAL E XAMPLE S. 41
der. They divide the apples equally, and AWhich ow e s the othe r
,and how much?
17 1 . H ow many me lodeons at 3 663 are wo4 piano s at 3 3 3 3 g172 . It is estimated that the public lands of the Un ited
States amoun t to 2265625 square miles ; if one -half of thiswas donated to vari ous purpose s, and the remainder wasso ld at per acre , what would be the n et income ?173 . It is e stimated that the annual loss to the Un ited
State s by intemperance is 398400000 . H ow many scho o lhouse s could be built
,and schoo ls sustained each year W i th
this sum,provided that the cost of a schoo l house and the
yearly expense s of the school,were each 3 1200 ?
174 . At a certain e lection 5000 vo te s w ere cast for thre ecandidate s
,A
,B and C. B had 400 more than A
,and C 3 00
more thanB . H ow many vo te s did A rece ive ?175. The income from the various shops in W e thersfield
State Prison for the year 1863,was 3 13 026 80 , the expendi
ture s, 3 120653 0 . NVhat was the net income ?
176 . The number of ve sse ls be longing to the U. S. Navywhich were captured by the rebels during 1863 was 12
,car
rying 48 guns, tonnage , 5947 the number de stroyed to prevent falling into the enemy ’s hands was 3
,carrying 29 guns
,
tonnage 2983 ; sunk in battle , 4 , w ith 28 guns, tonnage 2201lo st by shipwreck
,13
,w ith 61 guns
,tonnage 4854 . Required
the total naval loss during the year.
177 .The revenue collected fromrailroads is 3 cents for everydollar offare fromthis source 3 1029288 revenue was co llectedin 1863 . What amount was rece ived for passenge rs’ fare ?178 . In Rhode Island there are 400 school districts
,and
29600 children attend schools. Required the average attendance in each distr ict.179. One ‘ half the sum of two numbers is 500, and one
-halfthe ir difference is 3 00 . What are the numbers ?
42 AR ITHMETICAL E XAMPLE S.
180. The whole number of pupils attending the four normalschoo ls of Massachuse tts in 18622
,and the expenses of the
schoo ls were as fo llows Framingham,104 pupils
,expense s
,
3 3519 ; Salem,140 pupils
,expenses
, 34020 ; W e stfield,179
pupils, expenses, 3 3 119 ; and Bridgewater, 14 1 pupils, expense s
, 3 3 977 . What was the average expense per scholar ?181 . The condition of the banks of New York city
,April
16,1864
,was as fo llows : Loans
, 3 198703 699 ; specie,3 2 168760 ; circulation , 35779650 ; and depo sits, 3 168350790.
How much were the asse ts in excess o f the l iab i l itie s ?182 . During the year ending June 3 0
,1862
,the number
o f le tters exchanged b e tween the Un ited States and GreatBritain was 1485970 rece ived
,13 913 86 sen t ; be tween the
Un ited States and France,493 275 re ceived
,506461 sen t.
H ow many le tters did the exchange w i th Great Britain exce edthe exchange W ith France ?183 . The postage on mails sen t to Europe in 1862 amount
ed to 357353 3 .45 o n mails re ceived, 3570562 3 7 . The
po stage co llected in Europe was 3465744 2 3 , and the remainder was collected in the Un ited States. H ow much more
was collected in the Uni ted States than in Europe ?184 . The postage on mails transported by the Cunard l ine
in 1862 amounted to 352 1854 78 . What was the amount ofpostage on mails carried by other lin e s, the whole amountbeing as stated in Example 183 ?185. There were in the State ofNew York in 1862 , 11750
public schools,attended by 893 000 pupils. Required the
average attendance in each school .186 . In 1862 there were 554 stone schoo l houses in the
State of New York, 964 brick , 10004 frame , and a numberof log school house s, making the whole number 11750 . H ow
many less than one-fiftie th of the schoo l houses were built oflogs ?187. In 1862 there were 2 11452 12 acres of land in Ken
tucky, valued at 3 174187963 . How much had the land de
AE ITHM ET’
i oAL E XAMPLE S. 43
creased in value per acre since 186 1, when the average valuewas
188. Wisconsin sent into the army befo re Nov. 1,1863
,
3 4 infantry regiments,averaging 1001 men each ; 3 regi
ments cavalry,averaging 1290 ; 13 batterie s, averaging 16 1
o ne company sharpshoo ters, numbering 147 ; and 2441 re
cruits for old regiments. The quota under all calls up to thatdate was 44661. H ow much did the State lack of filling itsquota ?189. Russia exported gold and silver coin and bullion ,
in
1861,amounting to 5790355 roubles. The imports for the
same time w ere 7 13 83 95 rouble s. H ow much did the imports exceed the exports
,one rouble be ing worth 80 cents ?
190 . A teacher having a school of 144 ladies and 128 gentlemen
,divided it into the large st po ssible equal classe s, so
that each,class of ladie s should numb er the same as each
class of gentlemen . What was the number of classes ?191 . Ohio produced in 1862
,3 5442858 pounds of butter
,
worth on an average 20 cents a pound,and 2063 7235pounds
o f cheese,worth 14 cents a pound . What was the ir aggre
gate value ?192 . A farmer sold 3 4 bushe ls of cats and 26 bushels of
corn for H e rece ived fo r the corn 35 cents more per
bushe l than for the oats. What was the price of each perbushe l ?193 . The value of all the exports o f Russia in 1861
,by
maritime comme rce,was 13 7702 143 rouble s ; by overland
commerce,3 0473 888 rouble s. The value o f the imports for
the same year was,by maritime commerce
,1 15651243 rou
bles ; by ove rland comme rce,440280 13 rouble s. H ow
much did the value of the exports e xceed the imports, a rouble be ing worth 80 cen ts ?194 . The number o f le tte rs e xchanged be tw e en the United
State s and Europe,in 1862
,was 264403 9 sent
,and 2556624
rece ived, be ing a decrease of 945158 from the number re
44 AR ITHM ETICAL E XAMPL ES.
ported the previous year. H ow many le tters w ere exchangedin 1861
195. The Treasurer of Vermont made the fo llowing reportSept. 1
,1863 Balan ce in treasury
,Sept. 1
,1862
, 3 224250 .
4 1 ; receipts from o rdinary sources during the year, $774
3 273 0 on accoun t of the war, 3 1853 87 The disburse
ments were,for civil purposes
, 3 2816663 4 ; for war pur
po se s, 32358682 69 ; interest, 3 896692 1 . What balance did
the Treasurer repo rt ?196. In New York
,in 1863
,77862 men w ere drafted ;
53 109 were exempted,14073 paid commutation
,66 19 fur
nished substitute s,1504 failed to report. H ow many entered
the mil itary service ?197 . Jan . 1
,1863
,Pennsylvan ia had furn ished men for the
war as fol lows : 20979 3 -months men ; Reserve Corps, 15856 ; unde r ,
call of July 22,1861
,93 759 ; under requisition
o f July 7,1862
,403 83 ; under call of Aug. 4
,1862
,15100 ;
recruits fo r old regiments, 9259. The Adj utant Gen e ral,
allow ing for en l istments in other State s, reported the who lenumber 2003 3 6. H ow many did he estimate enl isted out ofthe State198 . There were 476203 vote s cast for two candidates for
governo r in Ohio,in 1863 . The majorityof the successful
candidate was 10 1079. H ow many vote s were cast for each ?199. A speculator had 2 10 acres of land, which he might
have so ld at $220 an acre, and gained $63 00 , but after ho ldingfor a time
,he sold it at a lo ss o f $3 150 how much per acre
did it cost him,and for how much per acre did he sell it ?
200 .A merchant bought 3 piece s of cloth of equal lengths
at $5 a yard he gain ed $35 on the whole cost, by selling 2pieces for $350 how many yards in each piece ?
46 AR ITHMETICAL E XAMPLE S.
10. D ivide 43
7“ 4
5X 53
b1 3 Of 93"
3y
1
83of 3
11. A can do a piece of work in 3 of a day ; B can do i tin 3 of a day, and C can do it in 13 days. In what time canall do it
,work ing toge ther
12 . If 5—1 lbs. of coffee cost $1 ,16 , what w ill 27} lbs. cost ?13 . A merchant had $9000 w ith which to purchase goods .
H e bought 20 pieces of shee ting,e ach contain ing 44 'yds.
,at
$ 12 per yard ; 400 piece s o f cal ico of 3 1 yds. each,at
per yard 25 pieces of cassimere,each containing yds .
,
at per yard ; 100 piece s of silk, each containing 293yds .
,at a yard. H ow much mo ney had he left ?
14 . In 1864 Ill ino is packed 1273 400 hogs,of an average
W e ight o f 200 pounds. H ow many car-loads would thesemake
,10 tons of 2000 pounds each loading a car ?
15. H ow long a train would all the cars necessary to shipthe pork mentioned in the preceding example make
,allow ing
25 feet for each car,there being 5280 feet in one mile ?
16 . A and B engage in trade. A furn ished T73 of the capital
,and B T93 . If B should transfer $3 793 of his capital to A,
the ir shares would b e equal . H ow much did each furni sh ?17 . H ow many time s can a vessel contain ing 1
4o f a gallon
be filled from 3 of a barrel contain ing gallons ?8 . Add the follow ing fractions 3 0of 3, 2 6 , 3 o f 3 of 5
,
3 o
l
f 3 of 3 3.
19. Bought a cord o f wood for $4 .625,a che ese for $7 .
563, and 14—9 lbs. butter at 25per lb. What was the co stof the whol e ?20 . A man purchased a number of lemons at 2 cents each,
and 3 as many at 3 cen ts each ; he so ld them all at the rate
o f 2 for 5 cents,and gained 25 cents. H ow many of each
kind did he purchase ?2 1 . A can do a p iece of work in 2 3 days, B can do i t in
3 3 days. In what time can both,working to ge ther
,do i t ?
AR ITHMETICAL E XAM PLE S. 47
22 . What number is that from which,if 7 3 be t
\
aken,the
remainder w i ll be 9323 . Find the sum of forty-n ine and three -tenths
,four hun
dred,and three mil lionths, subtract from i t two hundred
forty-six,and three thousandths, multiply the remainde r by
five thousand,and divide the product by four ten-thousandths.
24 . In New Jersey 13 7578 children attended the publ icschoo ls in 186 1
,and the total expenditure s for schoo l purpe
ses w ere 3540283 ; in 1862,13 2590 children were in the
public schools,at an expense of 3562259. H ow much more
was the expense per scholar the latter year than the fo rme r ?25. Pe ter can do a piece of work in 13 days, Martin in 7
96
of a day,and Jacob in 2 days . They commence the work
toge ther,but Martin ceases to labor after working 3 of a day,
and Jacob quits after having performed 3. of the task,when
Pe ter comple te s the work . H ow long
'
does Pe ter work ?26. If 3 horse s eat 2 71 bushel s o f oats in 2 days
,how
many horse s w ill eat 3 43 bushe ls in 8 days ?27 . From on e take tw o ten-mill ionths.
1 3 .
28 , R educg5
2
3f>
31 to a decimal fraction .
“
5“
8
29. In the Massachuse tts State Pr ison,fo r one year
, 3 3 0958
was paid for salarie s, 3 18468 for provisions, $7489 for clo th
ing, and 32643 2 fo r misce llane ous purpo se s ; 353 655wasrece ived fo r the labo r of the convicts. H ow much were thene t expense s of the prison ?3 0 . If a family o f 9 persons consume 98
31
I lbs. butter in43 weeks, how many pounds w ill each person consume per
w e ek3 1 . If 3 of a bushe l o f corn b e w o rth 3 of a bushel of
wheat,and wheat b e worth a bushe l
,how many bushe ls
of corn w ill $27 buy3 2 . After spending 3 , 3 of 3 , and of my money
,I had
$483 left. H ow much had I at firstf?
48 ARITHMETICAL EXAMPLES .
3 3 . What is the continued product of9
3 81X
1961X16 '
x3 64
?
3 4 . W hat number 1s that from which,
' if 11 be subtracted,
g of the remainder w ill be 42 ?3 5. H ow many yards of carpeting 1 1 yds. w ide would berequired to carpe t a room 6 7} yds. long and 52 yds. w ide ?3 6. Bought 12 yds. of cloth at 8.3 7% per yard , and agre edto pay of the cost in butter
,at per pound in
money,and the remainder 1n eggs
,at per dozen . H ow
many pounds of' butter and dozens o f eggs were required ?3 7. If tons of hay are sold for 810825, what w ill 1
ton cost ?3 8. What w ill yards of clo th cost at 85 per yard3 9. What i s the profit upon one mill ion spelling books
,at
per book ?40 . If 53 of a tub of butte r cost what w il l 9 tubsco st ?4 1 . Samuel Smi th has acres of land in one field
,
acre s in another,and acres in a third.
H ow much land must he purchase to have 640 acres42 . A farmer sold at one time 7 tons and 3 75 thousandths
o f a ton of hay,at ano ther time 12 tons and 3 125 t en-thou
sandths of a ton,and at a third time 13 tons and 3 125hun
dred-thousandths of a ton,at an average price of 88 per ton.
H ow much did he receive for the whole43 . W hat is the sum of decimal un its of the first order
,
of the second order,7,of the third order
,and 9—
2—3—5of
the fourth order ?44 . How many pairs of pants can be made from yds.
o f clo th,allow ing yds per pair ?
45. I purchased a quantity of grain, 3 of it being oats, at8.75abushel T
7,wheat
,at a bushel
,and the remain
ARITHM E T ICAL EXAMPLES. 49
der barley,at a bushel
,to the amount of H ow
much did I pay for the whole ?46. A owns 3 of a ship ; he se lls of his share for 81800.
What is the value of the ship ?47. A can perform a piece of work in 9 days ; A and B
together can do the same in 6 days ; A ,B and C wo rking to.
gether can do i t in 4 days. In how many days can B and C,
working toge ther, perform the who le48. What is the sum of 53 3, decimal un its of the firstorder
,65
55 of the second order, of the third order
,83 of
the fourth order,as of the fifth order
,and 3 ; of the sixth
order ?49. Multiply the sum of the quo tients of
.0103 .04735
.0005; 3 0 by50 . There are two numbers whose sum is 1
335, and whose
difference is 375. What are the numbers51 . A
,B and C own a furnace ; A owns
75
37; o f i t ; B owns
of i t more than C. What parts of the furnace do B and
C own respective ly52 . X and Y traded in company. X put in merchandisevalued at 88000, and Y put in 820000 cash. They agreed toshare the gains or lo sses equally . At the end of two years
,
the business proving unsuccessful,they dissolved partnership
,
and found the lo sses amoun ted to 81 1500 . What was eachpartner’s share of the remaining property ?53 . In the thirty-e ighth Congress, 1864 , the House of Rep
resentatives was divided into two parties,so that g- of the
number in one was equal to H’ the number in the o ther,and
there were 177 members. Required the number of eachparty.
54. W hat is the sum of the continued products of 8 x 4g
50 AR ITHM ETICA L EXAMPLES .
55. A man having 896, gave A 85 mo re than 5, of the
who le ; B 82 le ss than é of the remainder ; C 812 mo re than7} of the remainder, and the rest he gave to D. H ow muchdid each receive ?56 . The transactions of the Treasury of the State of New
York, in 1863 , w ere as fo llows : Balance in Treasury at thebeginn ing of the year, rece ipts during the year
,
81865628517 ; payments, 820703 5858 4 . H ow much lessin Treasury, Jan . 1
,1864
,than Jan . 1
,1863 ?
57 . M ultiply 1; ofT9, of 4} by T58 of of58. A teacher spends f; of his salary in board for himsel f
and family, 1
1
0“ in clo thing himse lf
,his w ife ’s clothing co sts 2
as much as his own,his daughter’s
, g as much as his w ife ’shis son ’s
,5; as much as his daughter’s, and he lays by 8115.
What is his salary ?59. The marble used in the Capitol extension
,Washington
,
had co st,Jan . 1
,1863
, 81029041, and the cutting and the setting of the same
, 813 73 749 more ; 19403 800 bricks had be enused
,worth per thousand, and the new iron dome cost
8900000 . Required the sum of these expenditures .60 . Divide 172 170063 by .0000009.
6 1 . What w ill doz . eggs cost at cents per doz . ?62 . Add n ine ten ~ tliousandths
,1000 and six-millionths
,3
and fo rty-seven ten mi ll ionths, 246 and tw enty-five -thousandths.63 . John Brown killed an ox , which, when dressed , we ighe d
1178 § lbs . , he kept gof i t for his own use, and sold o f the
remainder to Hiram Jones. What was the value of the re
mainder at 115cents per pound ?64.
A merchan t purchas ed 17 bale s o f co tton goods contain ing 5875yds. , at cen ts per yard ; he so ld 4 of i t at 1 12‘cts. per yard , and 3 o f the remainder at 125cts . per yard.
How much would he rece ive fo r what still remained at 13cents per yard and what profit would the merchant make on
his bargain ?
A R ITHM E'
M CAL EXAMPLES . 51
65. Fanny Church dispo sed of as fo llows : Shegave 8 of it to the San itary Commi ssmn
,of the remainder
to the Christia n Commission,and the remainder she divided
equally among 7 poo r women . H ow much did each womanre ceive ?66. What number must be multipl ied by 93 x 3 that theproduct may b e 100 ?67 A boy in flying his k ite lo st g o f the string
,then added
65 fee t and found that it was just g of the original length.What was the length at first ?68. A and B
,being
.
13 3 miles apart,travel towards each
other,bo th starting at the same time. They mee t at the end
o f 10 hours,and find that A has traveled 1—5mile s mo re than
B each hour. H ow many miles did each travel ?69. California cultivated
,in 186 1
,3 6 1350 acre s . of wheat,
which produced 8816940 bushels,and 20780 acre s of potatoe s
,
fromwhich 1298750 bushels w ere harve sted. Allowing theexpense of cultivating an acre of each to be the same
,the
wheat worth per bushe l, and the po tato es how
much more profitable per acre was the wheat than the po tatocrop70. A barre l holding 3 15gallons is 3, full ; 91 gallons be ing
drawn off,what part of the conten ts remain ?
1 3 3 8 . 4 2 7 . 5 4 7 37 1. Reduce to them lowest terms 3 7 ,and
l aaa3 7 0 4
'
72 . Three men,A
,B and C
,start from the same po int to
trave l around an island 100 mi le s in circumfe rence ; A trave l s252gmile s each day ; B , 1 15; mile s, and C, lagg mile s. R e
quired the least number of days in which all w ill b e toge therat the point of starting
,and how many time s each w ill have
l l’
wve led around the island .
73 . If at each stroke o f the piston rod of a locomotiveengine a distance of fee t b e passed over
,how many
stroke s must be made in passing fromNew York to Washing
52 AR ITHMETIC‘AL EXAMPLES.
to n, the distance be ing miles
,allow ing 5280 feet in
each mile ?74 If the circumfe rence of the truck whee l s of an enginebe 8 .8 fee t
,and of the d 1 ivers 2 1.3 fe e t
,how manymore times
w ill the one revo lve than the othe r,in running fi omNew
York to Albany,the distance being 150 miles ?
75. The enumeration of youths of school age in Ohio in1857 was 8 3 803 7 ; the enro llment of those in attendance was603 3 47
,and the average attendance
,3 50867 . In 1862 the
enumeration was 920890 ; enro l lment, 723 669, and averageattendance
,43 3 3 43 . Required the ’t
’fi re spective increase in
enumeration,enro llment and average attendance.
76 . 1f —30 f 4 of an acre of land se ll for 816 -
4 8“ what is 5
l 0 0 7
times of L S} of an acre worth at the same rate ?77 S. Smith being ask ed how many she ep he had
,replied
that he had them in 4 fields ; in the first there w ere 5 le ssthan J
,of the who l e number of sheep ; in the second 3, as
many”
as in the first ; in the third as many and in the fourththere were 3 0 sheep . H ow many sheep had he78 . A “an sp
ent for gqvul quantitie s o f butte r andlard ; fo r the butter he paid per lb . ,
and fo r the lard,
per lb. H ow much of each did he buy ?79. A had 8576 , which was 8156 more than % of 2 1 timesB’s money . H ow much money had B80. If 5of John’s marbles equals 4
,of Jame s’
,and bo th to
ge ther have 44 how many marble s has each ?
81 . If one yard of shee ting co st 183 cents, how many yardsmay be bought for82 . The State of Kansas paid 814009 67 for teachers’ salarie s in 1862
,and 81747 2 3 fo r incidentals. The district taxe s
amounted to 8103 818 1, and the scho o l fund , 84 148 45. H ow
large a school debt remaine d to b e provided for the nextyear83 . It is mile s from New York to Hudson
,and 74 {g
54 ARITHMETICAL EXAMPLES .
98. The distance from Boston to Worce ster is 44 mile s ;A
,starting from Boston
,travels 7411 of the distance ; B, start
ing from W orcester,travels 838 of the distance in the same
time. How far apart are they99. A merchant has 3 pieces of cloth
,
“contain ing respec
tively 288 yds. , 3 58 yds. and 4 18 yds . ; afte r se ll ing severalyards from each piece
,he finds he has left in the 3 pieces
658 yds. H ow many yards has he sold ?100 . What number is that to which
,if you add 8 of 8 of
itse lf, 8 of the sum w ill be 10 1
101. Bought yards of cloth,
yards w ide,for
what w ill yards,18yards w ide , co s t, at the
same price pe r square yard102 . A and B trade d w ith equal sums ofmoney ; A gained
a sum equal to 8 of his stock ; B lost 8220, and then hadas much as A . What was the original stock o f each ?
103 . James can do a piece of work in 8 of a day ; Henrycan do i t in 18’ days
,and John can do it in 8 o f a day . H ow
much longer w ill i t take John to do the work alone than i tdoes James and Henry wo rking toge ther ?104 . From a piece of cal ico contain ing 3 3 8 yds. there have
been so ld,at different times
,118 yds. , 78 yds ., 8
3
8 yds . and18 yds . H ow many yards remain ?
105. What number must be multipl ied byproduct may equal 1106 . The report from the Army of the Po tomac
,Feb . 1
,
1862,was as follow s : There w e re pre sen t for duty 1002 men
le ss than 8 of the whole army ; 162 1 men less than T]
? w ere
in hospitals ; 107 le ss than 71
1“ w ere in confinement ; 124
more than 1'
s“ w ere on furlough , and 1580 w ere unaccounted
for. H ow many men w ere reported for duty , in ho spital , inconfinement, and on furlough
,respectively
,and what was the
aggregate strength of the army ?
ARITHMET ICAL EXAMPLES . 55
107 . If T6? of a yard co st 810, what quantity wil l 8178purchase ?108. A merchant sold a piece of cloth for 824 , and thereby
lo st 8 of his purchase money . What part of his purchasemoney would he have gained had he sold i t for 83 4 ?109. George Hawkins leased 100 acres of land in M ississippi
,of the U. S. Government
,for one year ; his cotton crop,
raised upon 8 of the land,averaged 1 bale of 400 lbs . per
acre ; he planted corn upon the remain ing land,raising 458
bushe l s per acre. He sold the cotton at 50 cents per pound,and the corn at 75 cen ts per bushe l ; his expense s for farmingimplements
,labor
,and Government tax
,w ere just 8 the gro ss
receipts. What were the ne t profits for the year110 . Bought a horse and saddle for 8150 , and paid fo r a.
buggy 8 o f what I paid for the horse ; the saddle cost 8 thevalue of the horse . What was the price of each ?11 1 . A company, whose capital stock is divided into 1000
equal share s,conso l idate the stock into 3 00 equal shares .
H ow much larger would a share of the latter b e than one ofthe former size ?112 . If 22 boarders consume a barre l of beef in 63 days
,
how long would it last if 6 more were added to their number1 13 . If a man , by laboring 14 hours a day, can perform acertain piece o f work in 6 days
,how many days would it re
quire to do the same work,by laboring 12 hours a day ?
1 14 . In 1856, 405647 1 votes w e re cast for thre e presidential candidate s. Buchanan rece ived 497573 vote s mo re
,and
Fillmore 4673 09 vo te s less,than Fremont. H ow many vo tes
did each receive ?1 15. If a horse eat 198 bushels of cats in 878 days, how
many bushe ls would 14 horses eat in 3 0 days ?116 . Jame s Stow can mow a field in 6 days
,by working
10 hours a day ; his son George can mow the same fie ld in 9days, by working 8 hours a day. Ifbw long w ill it take them
56 ARITHMET ICAL E XAMPLE S.
both to mow the fie ld,provided they each w ork 6 hours
a day117 . An Ill inois
‘ farmer sold 2 129 bushel s of wheat f or8201 -53 ; 3 28 7
7
?bushe l s of corn for 8178 -5
8187 7
9
;bushels of
oats for H ow many bushels of grain did he sell , andhow much did he receive for the whole ?1 18 . The total expense s of public schoo l s in Pennsylvania,
in 1862,were 819553 15, and 3 85463 scholars attended schoo l .
The same year there were 68954 scho lars in the public schoo l sof Philadelphia
,educated at an expense of 8604100 . H ow
much were the expenses per scholar in the city more than in
the State at large ?119 . Bought
33 of a ten—acre lo t
,and so ld .g_ of what I pur
chased . H ow much did I se ll ?120 . Bought 8 lbs. hyson tea and 12 lbs. black tea. The
price per pound of the latter was g the pr ice of'
the former,
which was W hat did the whole cost ?12 1 . What i s the difference be twe en 4
31 5 yards
,and 159
whole yards ?122 . A lady spent of the day in sleep, 2, ln V i si ting, g, at
her to ile t, g, in read ing, and .2 hours each day in receiving
calls . H owmuch of her time remained for o ther o ccupations ?12 3 . A gentleman bequeathed é of his estate to his w ife, 7
}
of the remainder to his olde st son,and g of the re sidue to his
oldest daughter,whose share was What was the
value of the estate ?124 . The estimated value of all the gold throughout the
world in 1863,was 84860000000 ; of the silver, 85700000000 .
W hat part of this sumwas produced the same year, the annualproduct of gold being 8180000000 , and of silver
, 860000000 ?
125. A having lo4g! bushels of wheat
,sold
33of i t to B ,
who so ld 35, of what he bought to C, who so ld 4 of
'
what hebought to D . H ow many bushels did each purchase ?126 . A boy can do a certain piece of work in 3 3 days, and
ARITIIMETICAL E XAMPLE S. 57
a man can do the same in % of the time . H ow many daysw ill both working together require to do the work ?
127 . A grocer has 74 1- 36 gallons of beer, which he w ishes toput into bo ttle s, each holding ,
- o f a gallon. How manydozen bo ttles must he obtain ?128.
A garrison of 5000 men were besieged in a town,w i th provisions for three weeks, allow ing each man 16 ounce sper
.
day.Be ing re inforced by 3 000 men
, upon what allowance per day must the garrison be put, that the same provisions may last four w eeks ?129.
What w ill bales of co tton cost, each bale weighing cwt.
,at per cwt.
13 0 . What is the greatest common ' divisor of 408 , 11901445and 40 12 ?
13 1 . H ow many time s do e s the sum of 2 1 ; and 12 } cotain the ir diffe rence13 2 . In a certain school
,.3 75 of the pupils study arithm
‘
1
tic, .3 study grammar, .25 study geography , and the remain;der
,which i s 2 1, learn to read . What is the who le numb cl
of pupils ?13 3 . The public debt ofAustria in 1863 was 253 909083 6
florims,and her population was 3 47143 26 . What was the
debt per capita, a florin being worth 50 cents in Un ited Statesmoney13 4 . Divide 81000 among 7 boys and 9 girl s, giving to
each girl 5as much as to each b oy. H ow much do e s eachb oy and girl respective ly rece ive ?13 5. If 7 men or 11 boys can perform a piece o f work in
28 days,in what time can 1 1 men and 7 boys do the same ?
13 6. Four person s bought a house toge ther for 88250 ; Bpaid tw ice as much as A
,C paid as much as A and B
,and D
paid as much as A and C. H ow much did each pay “7
B elgium,the budge t fo r 1863 give s the to tal re
ce ipts at 155946790 f1ancs and the expenditure s at 150 120 ‘
45
58 AR ITHM ETICAL E XAMPLE S.
francs. H ow many more dollars w ere the receipts than theexpenditures
,5 francs be ing worth 98 cents U. S. money ?
13 8 . A man,go ing a j ourney of 4 18 miles
,finds at the end
of 5 days that the distance he has traveled is f} o f the remain ing distance. H ow many miles do e s he trave l per day ?13 9. A regiment of so ldiers
,consisting of 1025men
,is to
be furn ished w i th coats,each to contain 2 2
,yards
,yards
w ide . H ow many yards of cloth, 1g yards w ide, w ill l ine
them ?140 . H ow many times is 75 of con tained in .3 75
of
141 . A man having a cow and horse found that 4 loads ofhay would keep them both 6 months ; having dispo sed of hishorse he found that the same quantity of hay would ke ep hiscow 14 months. In what time did each consume 1 load ?142 . Bought a hogshead ofmolas ses contain ing 128 gallons
at a gallon ; paid fo r cartage,and lo st 16 gallons by
leakage . A t what price per gallon must the remainder besold to gain 3? of the entire co st ?143 . Jan . 20th
,1864
,Gen . B . F. Butler seized at Norfolk
,
Va.,48 barrel s of whiskey
,each contain ing gallons ; this
was sold for the U. S. Governmen t,
-
2
' at per gallon,and
the remainder at per gallon ; the partie s vio lating thelaw s of trade w ere also fined 81000 . H ow much did theGove rnment receive ?144 . The number of the Union army killed in the battle ofGe ttysburg was 515 mo re than r
'
ro f the who le lo ss ; the
number of wounded was 956 mo re than time s the numberkilled ; there w ere 6647 missing. W hat was the whole lo ss ?
145. A boy bought a slate, a book and a pen fo r 80 cents ;the pen co st 10 cen ts, and the book cost 1% time s as much asthe slate and pen . H ow much did each co st ?146. Divide 8870 among A,
B and C,so that of A’s
money shall b e equal to g of B’s,o r g of C’s .
ARITHMET ICAL E XAMPLE S. 59
147 . Bought a horse for 8115. At what price must i t b esold so that the gain shall be g of the cost ?148. By se ll ing a house for 82 175, my gain was - 3 of the
cost of the house . What did I pay for the house ?149. A grocer bought a cask o f sugar
,contain ing 400
pounds,for 83 2 ; a part of ' it be ing damaged he so ld the re
mainder for the cost per pound, and the reby gained a sum
equal to of his purchase money. H ow many pounds w eredamaged150 . A merchan t bought a bag of coffee
,con taining 80
pounds,at 15 cents per pound he also paid for roasting
it. For what must it b e so ld per pound to yield a profit ofthe cost o f the coffee, allow ing to each pound of a pound
forwaste ?151 The entire population of Denmark and the two Duchies
of Ho lste in and Schle sw ig,i s 2554870 ; Denmark contains 3
time s as many inhabitants as Holste in— 3 2706 ,and Schle sw ig
contains 13 4519 le ss than Holstein. What is the populationof Denmark and the Duchie s respectively ?152 . Bought a cask of nails contain ing 100 pounds at 4
cents per pound,and
,afte r reserving 15pounds for myse lf
,I
so ld the remainder at 53! cents per pound. H ow much did Igain153 . A can do .gof a piece of work in 4 days ; B can do 4
o f i t in 5 days ; C can do f, of it in 3 days,and D can do
of it in 1; days . Ho w long w ill it take them all to do i t ?
241 .006y
.0 125 .085155. A man owned seventy-five -thousandths of the stock
in a bank , and sold three hundred and twenty-five ten-thousandths of the who le stock . H ow much did he st ill own ?
154. Divide
156 . A mast stands g in the ground , in the water, and 3 3fe e t above the water. What is its length ?157 . I sold an article for 9, more athan it co stme
,to A
,who
60 ARITHMETICAL E XAMPL E S.
sold,i t to B for 810, which was g, le ss than i t co st him. W hat
did it co st me ?
158 . The number of postage stamps so ld in one year wasas fo llow s 53 893 792 one -cent stamps ; 151223 056 three-cent677200 five cent ; 3 925690 ten-cent ; 1053 900 twe lve -cen t ;650600 twen ty-four-cent ; 3 40000 thirty-cent ; and 24280
n ine ty-cent stamps. W hat was the whole number of stampsand the ir value ?159. Seven men engage to do a piece of work in a given
time, but three of them failing to come,the w ork was pro ~
longed 75days. In what time would the seven men havedone it ?
160. The report of the Normal School at Albany,N. Y .
,for
the year 1863,show ed that the number of male s was 1 le ss
than aof the who le number in atte ndance ; the number of females was 3 2 more than 9
3o f the who le number
,and 22 le ss
than 4 times the number o f graduate s ; and thre e -fourths o f
the entire number of graduate s w ere female s. What was the11 ho le number o f graduate s
,and how many w ere male s
161 . A man bought 3 barrel s of molasse s,contain ing re
spectively and gallons,at an average
price of per gallon . What was the who le co st ?162 . A person proposes to se l l his ho rse by lo ttery ; if the
price of the tickets be 83 each,he w i ll lose 820 on his horse
,
but if he sel l them at 84 each he w ill gain 820 . What wasthe value of the horse and the number of ticke ts ?163 . There is an island 27 mile s in circumference ; A,
Band C start from the same poin t
,and trave l in the same di
rection around it ; A goe s at the rate of 4 mile s B , 7 miles,and C
,10 miles per hour. In what time w ill they all be to
gether164 . What are all the exact divisors of 560 ?165. A person after spending 840 more than g of his
money, had 860 less than 4; of i t left. H owmuchmoney had he ?
62 ARITHMETICAL E XAMPLE S.
174. What is the sum of 45mill ionths, 45 thousandths, 45hundredths
,45 tenths
,and 45 uni ts ?
175. In 186 1, the revenue of the Post Office Departmen twas 89049296 40 , from 28586 offices ; in 1862 , i t was 8103 88
from 1997
3 office s . H ow much more was received,
on an average,from each office
,the latter year than the
former176 . A market woman w ished to sell a basket of orange s ;
her first customer bought - of what she had , and gave herback 5 the second bought g of what she then had, and gaveher back 10 ; the third bought 8 of the remainder
,and gave
her back 15; .the fourth bought of the re sidue, and gaveher back 20 ; after which she found she had 60 oranges left .H ow many had she at first ?177 . If 5of a yard of cloth cost 827-5, what w ill gof a yard
cost ?178 . The exterior semi-diameter of the exterior ring of
Saturn i s 88209 mile s,and of the in terior ring 75845mile s ;
the width of the interval betw een the rings is 1791 mile s,and
the space be tween the planet and i nterior r ing is 19089 mile s.What is the w idth of the rings
,the semi-diameter of the
plane t being 3 9580 miles ?179 . A and B can perform a piece of work in 1 days ; A
and C in_two days C and B in 22days. In what time wouldeach perfo rm the work alone
,and how long would it take
them to do the work toge the r ?180 . Bought 7640 brick
,at per 1000 ; 26789 fe e t o f
lumber,at per 100 ; and 986 fe e t o f pine boards, at
820 per 1000 ; I paid pe r 1000 for planing 23 463 fe e tof boards . What was the whole bill ?18 1 . There were 193 application s for admission into the
Normal School,at Albany
,in 1864 ; the number that passed
examination was 2 le ss than 4 time s the number that failed .
How many failed,and how many we re admitted ?
182 . A speculator gave 819550 fo r horses, and so ld a cer
AR ITHMETICAL E XAMPLE S. 63
tain number of them fo r 88925, at 8105 each ; by so do inghe lost 810 apiece . Fo r how much must he sel l the remaining horse s each, to gain 8425by the operation
183 . A and B together have i o f what A has, addedto 1
5of what B has, amounts to 8135. What have they each ?
184 . In 1862 , the export of petroleum from four ports wasas follows
,viz . from New-York
,6783563 gallons, valued at
8203 7413 ; from Philadelphia,2607203 gallon s
,worth 8529
575; from Boston , 8916 16 gallons, w orth 8457859 ; fromB altimore , 1120000 gallons, worth 8500000 . H ow manygallons wé re exported
,and of what value ?
185. What is the smallest sum of money w ith which I canpurchase e ither sheep at a head
,calves at cows
at 835, oxen at 870 , or horses at 8105?186 . A and B
,travel ing together
,started w i th such sums
o f money that 5of A’s was equal to {g of B ’s ; each spent812 , when % of A’s money was equal to of B ’s. H ow
much did each start w ith ?187 . The po int in the earth’s orbit farthe st from the sun i s
96600000 miles ; the point nearest, 93 400000 miles ; of themoon from the earth the farthest
,251760 miles ; the near
e st,22 1290 mile s . What are the gre ate st and least possible
distance s betw een the sun and the moon ?188 . From a cistern contaming 3 465gallons, barrels
,
o f gallons each,w ere drawn o ff H ow many gallons
remained ?189. A has 8647 , which lacks 83 3 of be ing 4 time s what
B has C is worth tw ice as much as A and B toge ther,lack
ing 872 . H ow much money have B and C respectively190 . A merchan t bought a number of bushels o f co rn ;
having so ld 6 bushels mo re than 9, of it to W . Smith,and 8
bushe ls more than of the remainder to J. Acke r,he had 20
bushels remain ing. H ow many bushels did he b uy191. The number of stamped envelopes sold in one year
64 ARITHM E TICAL E XAMPLE S.
w ere as fo llows : three-cent envelopes,22940 100 ; one -cent
,
2845000 ; four-cen t,70000 ; six cent, 40450 ; ten-cent
,13 1
750 ; allo w ing 5 cents as the co st o f paper and manufacturingevery package of 25 envelopes
,what was the whole number
sold and the ir value ?192 . Reduce 2, {13 , 55, 392 and 83 to their least common
denominator.193 . A
,B and C
,who can respective ly trave l 3
,4 and 5
mile s an hour,propo se to walk from Springfield to Hartford
,
the distance being 26 mile s. H ow many hours after A startsmust B and C each set out
,that all may reach Hartford at the
same time ?194 . In the battle of Chickamauga
,the number k illed was
485 more than g, the wounded ; the mi ssing w ere 13 morethan 3 time s the number killed ; the total lo ss being 15861,how many w ere killed
,wounded and missing ?
195. A farmer exchanged 50 loads of wood,each contain ing
of a cord,at per cord, for an .equal number o f bushels
of corn w orth a bushel,and of oats wo rth a bushel .
H ow many bushels of each did he rece ive ?196 . A has acre s in one lo t
,and in ano ther ; B
has acres less than 3 times as much as A ; C hasacres le ss than 5as much as A and B toge ther . H ow manyacres had B and C ?197 . The entire population of Connecticut in 1860
,was
460 146,and the products of industry w ere 883 0563 53 allow
ing of the enti re population to b e engaged in industrial pursuits
,what was the average value of the labor o f each during
the year ?198 . H ow many bushel s of corn must a farmer carry to
mill that he may b ring back 3 gbushel s, provided the millertakes {6 fo r to ll ?
3 2 1 7 7 1199. Reduce 3 6521 2 5 to 1ts lowe st terms.200 . John
,Henry and Charles have respective ly, 65, 91
ARITHMETICAL E XAMPL E S. 65
and 117 cents, w ith which they agree to purchase tops at thehighe st price that w ill allow each one to spend all his money .
H ow many tops can each buy?201 . Bought a quantity of lumber for 8785T36 , and of wood
for 83 47 33 ; so ld the lumber for 8649 :l and the wood for8589 -3. H ow much did 1 gain ?202 . Hudson County, New Jersey
,appropriated 83 723 08
for the education of 1750 1 children for one year. H ow muchwas appropriated for each child ?203 . Two men , miles apart
,traveled till they me t
each o ther,when
'
they found that one had trave led mile sfarther than the o ther. H ow far did each trave l ?204 . H ow many bushe ls of potatoes at 861, pe r bushel , will
pay for 6 5; bushe ls of wheat at per bushel ?205. The N. Y. Central R . R. Company owned
,in 1862
,
556 mile s in length of railroad,which co st for construction
and equipment, 83 1524226 . The New York and Erie R . R .
Company owned 446 mile s in length,which co st 835796902 .
H ow much was the average co st per mile of the o ne morethan of the o ther ?206 . The discharging pipe of a cistern has 32 the capacityof the rece iving pipe
,which w il l fill the cistern in hours ;
the rece iving pipe has be en Open4 73 hears,when the dischargingpipe is opened. In howmany hours after w ill the cistern b e full ?
207 . There were 2 187480 piece s of go ld , silver and coppercoined at the U. S. M int in one month
,valued at 8168908 ;
2 170000 were copper coins, and there were 12002 silver coins,valued at 86606 . What was the average value of the go ldco ins208 . If gof § of gof gof a ship be worth $5 of H, of -l-gof
75
3of her cargo
,how many times the value of the ship is her
cargo worth ?209. I exchanged 3 0 barre ls of molasse s
,each contain ing
3 4 gallons,at a gallon
,for 17 che sts of tea o f 24 pounds
each. H ow much did the tea cost me pe r pound ?
66 AR ITHM ETICAL EXAMPLES .
2 10 . A coal dealer sold 5 tons o f' coal for which.was 5as much as he rece ived for all he had left at per
ton. H ow many tons did he sell ?2 11 . A farmer sold
,in one year
,150 bushels of' oats at
per bushe l ; bushels of co rn at per bushelcords of wood at a cord ; 64534 pounds of wo ol
at per pound ; 23 head of cattle at an average price of
per head . H ow much did he receive for the who le ?2 12 . The number of railroad accidents
,in the U. States
,in
1862,was 5of the number of persons k illed by the accidents ;
and the injured,which were 877 , were 3 0 more than 2 time s
the number of acciden ts and killed together. What was thenumber of accidents
,and how many were k illed ?
2 13 . Six boys divided some chestnuts among themselves ;Jame s took
11
;of themwanting 6 ; Thomas took 6 le ss than
13; o f the remainder ; John took 5 le ss than i of what still remained ; Henry took 2 less than 1
‘of what then remained ;
William took 5 less than gof the residue, and George tookthe remainder
,which was 25. H ow many chestnuts were di
vided
2 14 . In 1858,9061504 bushels of wheat w ere sent out o f
the country ; in 1859,2849192 bushels ; in 1860
,4076704
bushels ; and in 1861,3 83 13 624 bushels. H ow many more
bushe ls were exported in 1861,than during the three previous
years2 15. What number i s that whose sixth part exceeds itseighth part by 20 less than i ts n inth part ?2 16 . A speculator sold a quantity of grain for 896 , and
gained 8 of what i t cost him. What part of the cost wouldhis gain have been had he so ld i t for 8100 ?
2 17 . A,B and C can perform a certain piece of work in
days ; A,B and D in 2981, days ; A,
C and D in 3 3 3days
,and B
,C and D in 42 days. H ow long would it take
each to do it alo ne ?
AR ITHM ETICAL EXAMPLES . 67
2 18. If a mason, in constructing a sewer, fe e t inlength
,begin w ith a diameter of 3 2 inches
,and increase .1 o f
an inch in every foot in length. How many times the diameter of the beginn ing will the end b e ?2 19. The sale s of spe rm oil for export and home use
,at
New Bedford,for the we ek ending Jan . 2 3
,1864
,w ere 3 488
barre ls,of gallons each
,at per gallon ; time s
the quantity for home use,was equal to 13 time s the quan ti
ty for export. What was the value of the exported oil ?220 . If 3 '
1‘
3Ttons of coal w ill last as long as cords of
wood,how many tons of coal will last as long as 13 11, cords
of wood ?22 1. A merchan t expended 83 84 for an equal number ofyards of six different kinds of broadclo th
,co sting re spectivelyper yard. H ow
many yards of each kind did he buy ?222 . H ow many rails
,o f the longest possible equal length
,
w ill inclo se a rectangular fie ld 9893 fe e t long by 8047 fe e tw ide
, w ith a straight fence six rails high ?223 . In 1863 the schoo l houses built of brick in the Stateof New York were
712the whole number + 16 ; the framed
school houses were 10 more than 10 time s the brick ; thestone
,3 less than 775 the brick, and the log schoo l house s w ere
3 3 less than i the brick . Required the number of each kind.
224 . What number is that who se part be ing subtractedfrom its the remainder w ill be 4 less than i the number ?225. A man dying, left to his oldest son 3
1 of the e state,in
creased by 71
6his daughter’s share to his youngest son gof
the e state plus 3, of his daughter’s share ; and to his daughterthe remainder
,which was 8700 less than the younger son’
s
share . What was the value of the estate ?226. A grocer has forgo tten the weight and first co st of a
b ox of coffe e ; he only recollects that if he had so ld it at 28cents a pound he would have gained8 2 .00, but if he had so ld
68 A R ITHM E TICA L EXAMPLES .
it at 2 1 cents a pound he would have lost Requiredthe number of pounds in the b ox and the first co st per pound.
3 Of ii 8 Of227 . The sum of
5and
4o f 2 25
i s equal to howmany0
‘
g‘
0
times the ir difference ?228. During the year 1861 , of the le tters exchanged b etween the Un i ted States and Great Britain
,170743 9 w ere re
ce ived,159 1644 w ere sent ; be tween the Un ited State s and
France,679184 w ere rece ived
,680577 sent . H ow many
letters did the exchange w ith Great Britain exceed that w ithFrance229. The rate of postage betw een the Un i ted States andGreat Britain was for each 3 ounce ; be tween the Un i tedState s and France
,allow ing the le tters to weigh ounce
each,how much greater w ere the rece ipts fo r postage
,be tw e en
the Un ited States and Great Britain than be tw e en the Un itedState s and France ?2 3 0 . A and B can do a piece o f work in 6 3 days ; B and C
in 12 days ; and A and C in 10 days . In how many daycould all working toge ther do it ?2 3 1 . A trader bought corn at per bushe l , and sold it
for H ow much did he lo se on every do llar he paidout ?23 2 . A boat which could move 14 mil es an hour in still
water, was accelerated 23 mile s per hour in gow g downstream
,and re tarded the same in coming up ; i t was 10 hours
longer in coming up a certain distance than in going down thesame . What was the distance ?2 3 3 . The difference be tw e en two numbers is 8
,and T
‘
Tofthe large r i s equal to 1, o f the smalle r. What are the numbers ?23 4 . J. Burke engaged to wo rk a year fo r 8180 and a suit
o f clo the s ; at the end of 8 months he was disabled,and re
ce ived for his wage s the sui t o f clo the s and 8110 . What wasthe co st o f the suit of clothes ?
70 A R ITHM ETICAL EXAMPLES .
took B 25days after they first set out. H ow far did B traveleach day244 . If 10 o xen
,o r 14 cows
,eat 4
75
3 tons of hay in 58 days,in what time w ill 4 o xen -
and 6 cows eat the same quantity o fhay245. In the State of New York 72 104 children attendedschool more than 10 months of a certain year ; 65161, morethan 8 months ; 1 15450 , more than 6 mo nths ; 176221, morethan 4 months ; 2403 28, mo re than 2 months
,and 2 17551
,less
than 2 months . H ow many children of scho o l age did not
attend scho o l at all,the whole number be ing 13 57047
246 . Six men can do a piece of wo rk in 73 days. H ow
soon after beginning must they b e joined by 2 more , so as tocomple te i t in 53 days ?247 . Bought a we stern farm for 81 1180 , and after expend
ing 8871 in improvemen ts , I sold one half o f it for 87740 , at818 per acre . H ow many acre s of land did I purchase
,and
at what price ?248 . How many times is the greate st common divisor of
4 3, 6 —3, 73 and contained in the least common multipleo f the same numbers ?249. When one do ll ar o f gold is worth 1593 cents, how
many whole do llars in go ld ought a brok er to pay for a tendo llar U. S. no te
,and how much fractional currency
250 . A hound ran 200 rods befo re he caught a fox ; 3 thedistance the fox ran before being caught was equal to the distance he was in advance when they started. H ow far in ad
vance was the fox,and how far did he run ?
251. The State Superintendent o f Schools in Pennsyl van iareported
,in 1862
,that 98 more than 3 the who le number of
school houses in the State were wholly unfit fo r use ; that 25more than tw ice this number were improvable , so as to answ e r for school purposes ; and the remainder, 4 13 3 , w e re
suitable in all respects. H ow many school houses in theState
ARITHMETICAL EXAMPLES . 71
252 . Twe lve men can do a piece o f work in 82. days ; howmany days may 3 remain away
,and ye t fin ish the work in
the same time,by bringing 7 more w ith them ?
253 . In 1860 , Virgin ia produced 123 96775lb s . of tobacco,
at an average value o f per lb. H ow many schoo lhouse s
,at a co st of 81150 , and how many churche s, at a co st
of 88550 , o f each an equal number,could b e built w ith the
proceeds o f the tobacco crop ?254. A b oy spen t one-third of his money for apple s , and
20 cents fo r nuts he then gave 10 cents more than one -fourthof the remainder for o range s
,when he found he had but 50
cents left. H ow many cents had he at first255. Divide 814500 betw e en A and B
,so that A shal l
have 3 as much as B , increased by 82500 .
256:In a lo t o f silve r change,wo rth 3 of the value
is in 50-cen t piece s, 3 of the remainder in 25-cen t p iece s
,and
the re st is made up of lo-cent,5-cent and 3 -cen t piece s
,o f
each an equal number. H ow many pieces of each coin are
there ?257 . If a cubic fo o t of gran ite w e igh pounds
,what
w ill b e the we ight o f a block o f gran ite fee t long,
fe e t w ide,and fe e t thick ?
258. The United State s has an area of 2819811 squaremiles
,and a population o f 3 1445080 . Euro
pe has an are a
of 3 757209 square mi le s,and a population o f 2688513 8 1 .
What is the diff e rence in area and populatio n
259. Divide the sum of 3 of 3 o f 28A? and 3
3 95; by the
3 105
3 4 3 983 2 3 128
27 875 snag260 . John and Jame s started toge ther and ran a race ;
when Jame s had run 80 rods, 7
1
7the distance John had run
was equal to the distance he was ahead o f Jame s . H ow
much did John gain on Jame s in runn ing 80 rods ?
con tinued product of
72 ARITHMETICAL EXAMPLES .
261 . A schoo l house which cost $980 is to b e paid fo r byfour men
,A
,B,C and D . It is agre ed that e ach shal l pay
acco rding to his nearne ss to the schoo l house . A i s tw i ce asn ear as B
,and B is
23 as near as 0
,who i s £
53 as n ear as D .
H ow much ought each to pay ?3 62 . If 14 men can perform a job in 27 days, in how manydays can they perfo rm the same labor w ith the assistance o f7 more men ?
263 . The value o f books printed in New Yo rk,in 1860
,
was 36920 102 ; of job wo rk, 3 2574529 ; of new spape rs
,
3 13 422254. The aggregate value of printing in the Un itedState s for the same period was 3 3 9678043 . H ow muchmore than one -half the value of the who le printing was donein New York ?2 64 . A can trave l around a certain island in 2 33 days, B
in days,and Cm 3 ; days . If they all se t out from the
same point, and trave l the same way, in how many days w i l lthey all mee t at the point fromwhich they starte d ?265. The total cost of maintain ing schools in the State of
New York , in 1863 , was 3 3 859 1592 1. The rural districtsraised by taxatio n 3503 18 12 8, by rate bills
, 3 3 63 74 10 5 thecit ie s raised by taxation the remain ing cost waspaid by the State School Fund ? What amount of moneywas received from the State ?266 . A man ‘laid out of his fortune in speculation
,and
put out on interest the remain ing $6800 ; at the end of theyear he had gained 757 as much by spe culation as he laid out,and his interest was g; of the principal . What was his fortune
, and how much did he gain during the year ?
267 . A man bought 2400 bushels of corn ,at a bushel ,
but in measuring it he found that he had more bushels thanhe paid for
,and that he had gained bushels for every
hundred . He sold the same w ithout delay at a bushel.H ow much did he make by the transaction ?
AR ITHM ETICAL EXAMPLE
268. A man has 2 horse s and a saddle ;placed upon the first horse
,valued at $60 , i
141 time s the value of the second horse
,but i
second horse,i t w ill make his value tw ice th
Required the value of the saddle and the second horse .269. In 1861
,there w e re 2819811 square mile s
,of 640
acres each,in the Un ited State s ; and there w ere 1 155510
farms,of 2 15 acre s each
,under cultivation . H ow many
acres w ere still uncultivated ?270 . The above farms w ere each valued at an average of
$5756 , and upon each farm there was an average of $2 13 inmachinery and implemen ts. What was the aggregate valueof the farms and implements ?27 1. Bo ught a bale of cloth for and dispo sed of i t
for fir the cost, by which I ~lo st on a yard. H ow manyyards w ere there in the bale ?272 . The re i s a cask contain ing brandy and water ; is of
the who le 4 gallons,i s brandy
,and 4 of the whole 2
gallons is water. How many gallons of each ?273 . A had 2, of g. o f 3 fai times $3 1448 , and paid 3 of }g of{70of i t for a farm. H ow much money had he remain ing ?274 . Bought lb . of sugar for $ 3 75. For how much
must I sell lh.,to gain the cost of .25 of a lb .
275. The New England State s had sen t into the army,Jan .
1,1863
,183 73 2 men ; the Middle State s, 453 3 86 the We st
e rn States,103 887 more than the M iddle State s ; the Bo rder
State s 10 1877 less than the New England State s . Of thewho le number
,9156 1 were three -months men
,673 35 nine
months men,and 4857 1 were enl isted for irregular periods ;
the remainder enl isted for three years. H ow many o f thisclass were there ?276 . A man divided $670 among his 3 sons
,so that g the
share of the first was equal to the ghare of the second , andto gthe share of the third . Required the seve ral share s.
4
74 ARITHMETICAL EXAMPLES.
277 . Bought 24 tons of hay, at per ton,for § ofwhich I paid sheep , at $3 ? each, and for the remainder I paidbutter
,at $.l9% per pound. H ow many sheep and how many
pounds of butte r did it require to pay the debt ?278 . Bought 17 chests of tea
,each con taining 59 pounds
,
at a pound,and gave ln exchange 118 bags of wheat
,
each contain ing ’
3 .4 bushe ls. What was the value of thewheat per bushel ?279. The value of the flour and meal produced in theUn i ted States
,in 1860
,was $224000000 ; of cotton goods,
three mi llion of dollars more than one-half the value o f thecorn and meal ; of boots and sho e s, E38 the value of cottongoods ; of clothing, the value of the boo ts and shoe s ; ofprinting
, 2 the value of the clothing. H ow much did the
sum o f the value s of the printing,and boots
,and shoes
,exceed
in value the co tton goods ?280 . The circumference o f a circle i s alwaystimes the diameter. H ow many revolut ions w il l a ‘carriage
A whe el,which is 3 1, fee t in diame te r
,make in gomg a distance
o f mi les ?281. A father divided a piece of land among his thre esons . To the first he gave acres ; to the se cond , 753 of
the who le ; and to the third , as much as to the other two .
HOW‘many acre s had the third ?
282 . The British army in India,in 1863 , consisted of 7062
cavalry ; tw ice as many artillery, lacking 124 ; and 4 time sas many infantry as artill ery
,lacking 1 163 . The cavalry in
the home army w ere 66 mo re than the artille ry in the Indiaarmy
,and the infan try 2968 more than 9 time s the home cav
alry. What was the aggregate strength of the home and
of the India army283 . A market woman bought a numbe r of peache s at therate of 2 for 1 cen t
,and as many mo re at the rate of 3 for 2
cen ts,and so ld them all at the rate o f 5 f or 3 cents
,gain ing
4 cents. H ow many peache s did she buy
AR ITHMETICAL EXAMPLES. 75
284. A tree 164 feet high,in failing was broken into two
piece s,of such lengths that 3 of one piece equaled é of the
other. Required the length of the pieces.285. In Wisconsin, the number of stone and brick schoo lhouses
,in 186 1
,was 3 76 ; of framed, 2478 of log
,1357 ;
the average co st of these buildings was What wasthe cost of all the school houses ?286 . If 3 ' yds of cloth
,1 3 yds. w ide
,co st $3 .46g, what
w ill be the cost of 42 1 yds ., L; yd .s w ide ?
287 . A piece of land was divided into two parts,so that 5
the first was equal to j, the second . The difference be tweenthe two parts was acre s. What was the wholeamount
,and what were the parts
288. What is the value of the follow ing expre ssion8 3
,22
,2 2.
5
1+3 fl
7 2°f <97
4 2.
,
X3 9
289 . A garden whose breadth 1s 9
1 3
,rods and who se length
is 1gi ts breadth, has a wall 3 3 fee t thick around it. Whatwas the cost of digging a trench 2} fee t deep , in which to laythis wall
,at 12: cents per cubic foo t ?
290 . There were 3 8068 children attending schoo l in 6 14districts in Califo rnia
,in 186 1. The who le co st of schoo l s for
the year was $470 1 l5.24 . What was the average numberattending in each district
,and what the average expense per
scholar ?291. Three horse s start from the same po in t
,and at the
same time,upon a race-course 3 00 rods in circuit ; the first
horse passing over 5the circuit, the second the third12,in
a minute . In how many minute s w ill they all b e toge theragain
,and how far w ill each have trave led ?
292 . Bought 4 bushe ls of wheat,and 3 § time s as many
bushels o f corn ; fo r the former I paid 5as many do l lars perbushe l as there w ere bushe ls of the latter
,and for the latte r
3 as much pe r bushel as for the former. Required the priceof cach
'
per bushel, and the, who le co st ?
CHAPTE R IV
1 . The source of the river Volga is 550 feet above the leve lof the sea ; after a course of 2000 mile s i t emptie s into the
Caspian sea,which is 83 fe e t be low the surface of the ocean .
H ow much is the average fall, pe r mile , o f the river ?
2 . A physician bought by Avo irdupo is W' eight,15 lb .
Opium at 4 cents a dram,and so ld the same by Apothecarie s’
We ight,in do se s of 10 grains each
,for 25 cen ts per do se .
H ow much did he gain ?3 . The amoun t of money in the Sub -Treasury in New
York,Jan . l st 1864, was 8128989268 9 ; the amoun t re ce ived
in January,on account of Customs
,was 8617960551 ; of
Loans, 333 7463 8959 4 ; o f Internal Revenue
, 3 2275409 67 ; ofTransfers
,o f Paten t Fee s
,ofM iscel
laneous, 341643522 7 of Post Office Department
, 3 108982 .
51 and the amount paid out in Treasury Drafts was 3483 438066 6 ; in Po st O ffice Drafts, 3 82663 06 . H ow much re
mained in the Treasury,Feb . l st, 1864?
4 . Hovir much land in New Yo rk at per square foo tw ill aeooooo buy ?5. The population of London
,in 1860
,was 2800000 ; the
number of deaths dur ing the year was 63 644 ; the populationofNew Yo rk
,at the same t ime
,was 805600
,and the number
o f deaths,18120 . H ow many more deaths pe r mill ion in
London than in New York6 .A man and his son w alk from Hartford to New Haven
,
a distance of 3 6 mile s ; allow ing that the man passe s o ver adistance of 2 ft. 9 in . at each step , and the b oy a distance o f
1 ft. 10 in .
,how many more steps does the b oy take than the
man .
78 ARITHM E TICAL EXAMPLES .
4101 T. 8 cwt. 3 qr. 3 lb . ; if copper was worth 20 cents perpound
,of how much greater value was the amount produced
in 1863,than in 1862 ?
16 . In the Maine House of Representatives in 1863,the
number of lawyers was 5more than the editors ; the clergymen
,2 more than the lawyers ; the merchants 17 more than
the clergymen,and 17 less than the farmers
,who were 1 more
than 9; the whole number. W hat was the number of eachclass17 . A man took 5 loads of turn ips to market
,each load
containing 16 bags,and each bag 3 bushels ; he sold them for
20 cents a bushel,and received in paymen t 4 boxe s of sugar
,
each box contain ing 8 papers,and each paper 15 lbs. W hat
was the price of the sugar per pound ?18 . Sold 72 yds. carpeting at a yd.
,and gained
thereby 3 18. H ow much did it cost me per yard19. A merchant carried on business thre e years ; the first
year he gained a sum equal to 747 of his original capita‘
l thesecond year he lost 1 of what he had at the end of the firstyear ; the third year he gained 7
36of what he had at the end
o f the second year ; he then had 3 14625. H ow much had hegained in the three years ?20. A farme r exchanged 26 bu. 1 pk . 6 qts . of cats for 22bu . 4 qts. of salt. What quantity of o ats must be broughtto the same market by a farmer who w ishes to get 73 bu . 3
pks. of salt ?2 1 . Divide 63 7 A. 3 R. 8 P . 11 sq. yds. 4 sq. ft. 16 sq. in .
by 16.
22 . A pedestrian,in train ing for ‘a foot race
,traveled 75mi.
3 fur. 3 7 rd. 5yd . 2 ft. 10 in. the first w eek ; the se cond w eek,
89 mi. 3 fur. 9 rd . 2 yd. 1 ft. 10 ih . ; the third w e ek,127 mi.
6 fur. 9 rd. 1 yd. 3 ft. 10 in . H ow far did he trave l in the
three w e eks ?23 . If a person count 90 a minute f or 10 hours each day,
how long w ill i t take him to count a mill ion ?
AR ITHM ETICAL EXAMPL E S. 79
24 . Bought a lot 25rods long and 20 rods w ide for $10000
,and so ld the same at 25 cents per square foot . H ow
much was my gain ?25. Simplify the following fractions
1
X7
X207
.003 ; 500
.og 25
26. A cellar is 26 fee t long, 18 feet w ide, and 7 feet deep.
H ow much earthmust be removed to make it 28 fee t long, 2 1feet w ide
,and 8 fe e t deep ?
Q 27 . H ow many square yards in ”
the walls of a room 40 fee tlong
,3 15feet w ide and 12 fee t high ?
28 . A person, be ing asked the time o f day,repl ied 11g
times the time past noon is equal to times the time tillmidnight.” What was the time ?29. I purchased some pens at two for a cent, and time s
as many at 3 for 2 cents ; I sold them all at the rate of onehalf a cent each
,and lost 15 cents by the transaction . H ow
many of each kind did I buy3 0 . The market value being the same in both State s
,a
farmer from New Jersey exchanged 50 bushe ls of buckwheat,
worth $1 31 a bushel,w ith a farmer in New York
,fo r oats
,
worth abushel,which he sold in his own State for cash.
The exchange being made by weight, in whose favo r was thedifference
,and how much in cash value ?
3 1. What w ill 43 bale s of cloth co st, e ach bale con tain ingyards
,at 5 a yard ?
3 2 . A man worked 3 months,25 days each month
,10
hours each day,for an hour
,and received in payment 2
loads of grain,each containing 15 bags of 25bushels each .
What was the price of the grain per bushe l3 3 . Ib ought 3 97 barrels of flour
,at per barrel ;
290 bushels of corn, at per bushel ; 48 barrels of bee f,
80 ARITHMETICAL EXAMPLES .
at per lb . ; 170 barrels of pork, at per lb . ; and
225 cords of wood, at per cord foo t. What was thedifference in value be twe en the sum of the co st of the flourand the corn , and the sum of the cost of the other articles ?3 4 . H ow many tons of hay , at per cwt., must be givenfor 35 cords of wood, at per cord foot ?35.
It is estimated that the Falls of Niagara have receded50 yards w i thin the last 40 years . H ow long at this rate hasit taken them to recede from Lew iston, 6 miles below theirpresen t site ?3 6. The amount expended in work upon the canals in New“
Yo rk,in 1863
,was as fo llow s, viz. Champlain Canal , 348
Black River,
Erie, 3 15143542 ; Osw ego ,
3 15456 02 ; Cayuga, 3 1975558 ; Baldw insville, 32561588 ;Chemung
, 3 15083 2 0 ; Crooked Lake, 3 2889562 ; Chenango ,3 1693521 ; Gene see Valley, 3 88292 75; for work done byCanal Superin tendents
, 3 107626 51 . What was the wholeamount ?3 7 . The total cost of engineering upon the above men
tioned canals was 3 3 1223 1 1 . H ow much was expended inwork for 3 1 in engineering ?3 8. What part of 5 da. 23 h . 58 min . i s 4 da. 6 h . 50
min .?
3 9. Bought 7000 bushels of corn in Chicago at abushel . I shipped the same to Buffalo
,and sold it at an ad
vance of 20 cents per bushel ; the expense s for fre ight andhandling the grain were 3500 the corn being bought and so ldby weight
,how much did I gain or lose ?
40 . Nineteen lots of equal size contain 159 A . 2 R . 17 sq.
rd. 25 sq. yd . 8 sq. ft. 13 0 sq . in . W hat is the value of onelot, the land being worth half a dollar per square foot ?4 1. A spent
(1,his money and gave away 3 20 ; he then
spent g the remainder and gave away 3 10 less than 5of whatthen remained
,and found he had 348 left. H ow much had
he at first ?
ARITHMETICAL EXAMPL E S . 81
42 . The amount o f chee se made in the State ofNew York ,in 1860
,was 48548288 lbs. Suppo se each cheese to we igh
64 1b s .,and to b e 20 in . in diame ter
,how many mi les in
length w ould they extend if placed in a line ?43 . Thirty-two men agree to build 14 mi. 5 fur. 3 4 rd . 6 ft.
of road ; when the wo rk is done they employ 8 moi’e men.
What distance doe s each man construct44 . The total vote for Governo r in Kentucky, in 1863 , was
85695, of w fi Bfi fifiéflef thfi fibcessful candidate, rece1ved50917 more than Wickliffe , his rival ? How many votes dideach receive ?45. A housebreaker, having b e en brought before a iudge ,i t was proved that be had stolen property to the value of £912 s. 9d. 3 far. ; he was sentenced to pay at the rate of £9 12 s .
9d. 3 far. for every pound stolen . H ow much was the fine ?
46. A and B started together by railroad from‘
Philadv l
phia for P ittsburg,the distance being 3 56 mile s ; A trave le d
by express,at the rate of 3 0 mile s per hour ; B by mail
train,at the rate of 25mil es per hour ; C left P ittsburg for
Philadelphia,at the same time
,by fast line
,at the rate of 3 2
miles per hour . H ow far from Philadelphia were A and Brespectively , when C passed them?47 . What is the value of .6923 828125 cwt. of coffee at
3 833
; cents pound ? a,a48 . A wood-dealer del ivered fac
tory ; i t was in thre e piles, the first was 18 ft. 6 in . long,7 ft.
6 in . high, and 4 ft. w ide ; the second was 16 ft. 9 in. long
,6
ft . 9 in . high,and 4 ft. 6 in . w ide ; the third was 20 ft. 3 in .
long,7 ft. 4 in . high
,and 4 ft. 6 in . w ide. How many cords
were del ivered49. A farmer so ld 19 bushels of rye and 23 bushels of barley for he rece ived for the rye 15 cents more pe rbushel thaP dr the barley.
~ What was the price of each perbushel50 . Sold 4 village lots the first contained of g o f an_1
3
82 AR ITHM ETICAL E XAMPLE S.
acre ; the second rods ; the third 71of an acre
,and the
fourth gof gof an acre. H ow much land in the four lo ts ?51. A man bought a horse and two carriage s ; for the firstcarriage he paid $250 ; if this sumw ere added to what hepaid for the horse, i t would amount to o f the sum he paidfor the second carriage ; if the sum he paid fo r the horse w ereadded to the sum paid for the second carriage
,it would
amount to three time s the sum paid for the first carriage .
W hat did he pay for each ?52 . H ow far does a team walk in plow ing an acre
,allow
ing 10 inches for each furrow ?53 . The aggregate rece ipts of the railroads in Pennsylvan ia
fo r 1863 w ere 3540523571 the eH ow much w ere the ne t earn ings ?54 . H ow much beef; at 7d. per rece ive
for 27 lb . 12 o z . of butter at l s . 9d. per pound ?55. A ship at the equato r in 20° 3 0 ’ W . longitude
,sailed
due We st,until its longitude was 3 6° 18 ' W . H ow many
statute mile s did the ship sail
56 . There w ere three candidate s for the office of Mayor inthe city ofNew Yo rk
,Dec. 1863
,and there w ere 7 1 10 1 vote s
polled ; the successful candidate received 6524 vo tes morethan on e competitor, and 973 8 more than the other. H ow
many votes did each receive57 . If a town ,
10 mile s square, be divided equally into 3 00farms
,what w ill b e the size of each farm?
58. H ow much must be paid for a pile of wo od 12? ft.long
,ft. w ide, and 35ft. high , at per cord foot ?
59. In the city of Springfield, Mass ,for the year 1863 the
number of scho lars in the mixed schools was 272 , which was6 of the number in the primary school s ; $2 of the number inthe primary schools were equal to the number in the intermediate schoo ls
,which was 25time s the number in the gram
mar schools ; the number in the high schoo l was 1 less than
AR ITHM ETICAL EXAMPLES . 83
72
87the number in the grammar schools ; required the number
in each grade of school s.60. The annual expense of the schools in the above-men
tioned city was 82 3 3 62 50. Now if the expense per scholarwas the same in the mixed schoo ls as in the primary
,and in
the intermediate 1; times as much ; in the grammar schoo ls1 ; times as much as in the intermediate ; and in the highschool time s as much as in the grammar schoo l. W hatwas the expense of each grade of school for the year ?61. A gentleman travelling west from Boston
,which is
7 1°
3’ W. longitude, finds, on his arrival at St. Louis, that his
watch is 1 h. 17 m. 24 see . faster than the time at the latterplace ; i f his watch has k ept accurate time, what is the longitude of St. Louis62 . What w ill b e the cost of 9 gal . 3 qt. 1 pt. 2 gi. of kerosene oil at 6s . 8d. per gal . , New York currency ?63 . Express in acres and the decimal of an acre the areaof 49 square lots
,each measuring 5rd. 8 ft. 3 in . on a side .
64 . The number of cents coined at the U. S. mint in Philadelphia during the month of January
,1864
,was 220800 ; the
silver coinage was 5the value of the cents, and also 3 the valueof the silver deposits ; the deposits of silver were 20 dollarsmore than
717of the gold co inage
,which was gigof the go ld
deposits. Required the sum of the deposits and of the coinage,
65. Bought 48 bushels corn at 6s . 6d. per bushel, New
York currency, and sold the same at 58 . per bushe l, New
England currency. H ow much did I gain on the who le ?66 . What is the value of a fie ld 15 ch. 75 1. long
,and 12
ch . 50 1. w ide,at $64 per acre ?
67 The popular vote for president in 1860 was 4680193 ;Lincoln rece ived 491295 more vote s than Douglas
,who re
ce ived 527204 more than Breckinridge ; and Breckinridgerece ived 2573 22 more than Bell. H ow many did eachrece ive
84 AR ITHM ETICA L EXAMPLES .
68 . Reduce 5of5of 455lb . to the decimal of a short ton .
69 . Suppo se the Erie canal to b e 60 feet w ide,and 6 feet
deep,how many miles in length w ill it require to make one
cubic mile of water ?70 . In the packing-yards of New Yo rk there were
,Feb . 1
,
1864,88180 bbl . of pork
,and 107643 bbl . of beef ; the aver
age value of the pork per barrel was of the beef,5. What was the difference in their entire values ?
71 . There is a house 40 feet long,and each s ide of the roof
is 20 feet w ide ; allow ing each shingle to be 4 inches w ide ,and 18 inches long
,and to l ie one -third to the w eather
,how
many half-thousand bunches w ill be required to cover theroof ?72 . H ow many bushe l s of grain w ill a b in con tain that i sft. long, ft. w ide
,and ft. deep ?
73 . The difference in longitude be tween London and St.
Louis is 90° at a ce rtain time each day it is as much pastnoon in London as it lacks of noon in St. Louis. What i s thetime in St. Louis74 . At what time between 8 and 9 o’clock is the minutehand as far beyond the V mark as the hour-hand is beyondthe VIII mark ?75. A gentleman having 860, paid in Boston 14s. 8d. for ahat
,18s . 6d. for a vest
,and for a coat ; go ing to New
York,he
,
paid for his fare,and in the city bought 10
books at 7s . 6d. each ; gave 3 s . 9d. to a blind man ; and paid17s . 3 d. hotel bill . H ow much money had he left76 . On an acre of ground there w ere erected 2 1 buildings,occupying on an average 3 sq. rd. 112 Sq. ft. 8 sq. in . H ow
much of the acre remained unoccupied77 . Co lt’s Armory, Hartford, Conn .
,which was destroyed
by fire,February 4
,1864
,was insured in New Haven to the
amount of 820000 , which was 533 the insurance in Providence,and 5the insurance in Springfield ; the amoun t insured inthese three cities was 5the in surance in Hartford ; and the
83 ARITHM ETICAL EXAMPLES.
85. Bought 3 00 bushe ls of wheat in New Jersey at 8s. perbushel
,and sold the same in New York at 8s . 6d. per bushe l .
H owmuch did I lose ?86 . From5of 3 65)I da., and 3 of 5; wk .
,take 3} of 82min .
87. In 1863 the imports o f sperm oil w ere 65055 gal . ; ofwhale oil
,62974 gal . ; of whalebone, 488750 lb . the average
price per gallon of the sperm o il was of the whaleoil
,and of the whalebone
,per pound. What
was the total value of the whaling business for the year ?88. A man having a fie ld 3 0 rods square
,sold 25 square
rods to one of his neighbors,and 20 rods square to another.
What is the value of the remainder at 8175per acre ?89. If corn be rated at 7s . 6d. per bushe l in Maine , at whatprice in the currency of New Jersey must it be sold to gain
on 90 bushels ?90 . A grocer bought 15bbl . of dried cherrie s
,each barre l
contain ing 3 bushe ls,at 86 pe r barrel, and dire cted his clerk
to re tail them at 10 cen ts a quart. By mi stake he used abeer measure. H ow much did the grocer lose by this mistake ?91. What part of a leap year is past at noon on the Fourthof July92 . H ow many bale s o f cotton, of 400 lb . each
,at 3 6 cents
per lb .,are equal in value to 18 hhd . of sugar of 1500 lb .
each,at 8 cents per pound ?
93 . There i s a park 3 00 fe e t square ; if a walk 4 feet w ideb e made around it, w ithin the inclosure
,how many square
yards w il l i t con tain ?94 . If a gallon of distilled water weigh 8 lb. 5 oz. dr.
,
what is the weight of 17 gal . 3 qt. 1 pt. 1 gi.95. If
,when wheat is worth 6s . 3 d. per bushel , a 5- cent loaf
weighs 24 o z . ,and allows the baker 15cents a loaf for his labor,
what should it w e igh when wheat is 8s. 4d. per bushel,to
afih rd him the same profit on a loaf?
87
96. The distributing reservoir 0square on the top
, and 45fe e t high.
dicular,what would b e its capacity in w ine gallons ?
97. At 35cents per foot, what w ill be the cost of 12 planks,each measuring 56 ft. 9 ’
98. There is a garden 6 rods long and 5 rods w ide,w i th a
ditch around it 5 ft. w ide and 65ft. de ep, the earth fromwhich was thrown upon the garden in uniform thickness.H ow much was the surface elevated ?99. In the battle of Antie tam
,the number killed in the
Un ion army was 10 1 less than 5the who le lo ss ; the prisone rswere 35more than 5 the killed
,and the wounded w ere 144
less than 35times the sum of the killed and prisoners . Whatwas the total lo ss ?100. In the same battle i t was estimated that the number
killed in the rebel army was equal to the number takenprisoners ; and the sum of these was 35of the wounded ; theto tal rebel loss was 193 2 less than twice the Un ion lo ss .t at was the number killed
,wounded and pri soners ?
101 . Divide 100 into two such parts that one shall be 12 1greater than the other ?102 . A man paid for a certain pile ofwood . Meas
uring it he found that it contained 5 Cd . 6 ed. ft.,12 cu . ft.
W hat did the wood cost him pe r cord ?103 . A room i s 18 ft. 6 in . long, 14 ft. 6 in . w ide
,and 9 ft.
9 in . high ; there are four w indows in the room,each 6 ft.
long by 3 ft. 3 in . w ide,and two doors, each 6 ft. 9 in . high
by 2 ft . 10 in . w ide ; the base is 9 in . w ide. What will bethe co st of plastering the room
‘
at per square yard104 . An estate worth £3 680 is to be divided as fo llows
The w idow has 5of the who le , and the remainder is to b eequally divided among 6 children. How much doe s eachchild receive ?105. If 6 lb . of tea be worth 14 lb . of coffe e
,and 7 lb . of
88 AR ITHMETICAL EXAMPLES .
coffee be worth 24 lb . of sugar,how many pounds of tea can
be bought for 16 lb. of sugar ?106. A person was commissioned to lay out equal sums in
the purchase of spelling books,grammars
,algebras and ge
ome trie s,and to expend as l ittle money as po ssible ; he found
spelling books at each,grammars at algebras at
andgeometries of two styles of binding ; one atthe other at of which he impruden tly chose the cheaper.H ow much money was thereby unnecessarily expended
,and
how many more books than was necessary did he purchase107. A blacksmith bought 20 tons of iron at 880 per ton ;
he sold 6 T. 15 cwt. 3 qr. 9 lh.,at per pound ; having
made 3 522 horse shoe s,averaging 2 lb . 8 oz . in weight
,and
sold them at each,he disposed of the remain ing iron at
898 per ton . H ow much was his gain ?108. H ow much w ill i t cost to carpet a room 2 1 ft. long,
15 ft. w ide,w ith carpeting 5of a yard w ide , at per
yd109. A goldsmith manufactured 1 lb . 10 oz . 15 pwt. o f
gold,which cost him 816 per oz .
,into rings
,each w e ighing 2
pw t. 12 gr.,which he so ld at each. H ow much did
he receive for his labor ?110 . W hat decimal expression i s equivalent to
3 8 of of 48
2 305
111. Bought 12 T. 3 cwt. 2 qr. 20 lb . of sugar at per
cw t. What was the cost1 12 . If a man could walk around the earth in 4 yr. 13 7 da.
15 h . 48 min .,how long w ould it take him to walk one de
gree,allow ing 3 655days to a year ?
1 13 . A merchant owned 55of a stock of goods ; 5of thewhole stock were destroyed by fire , and {75 of the remainderdamaged by water. How much did the merchant lo se, provided the uninj ured goods w ere sold at cost, fo r 84200 , andthe damaged at half the cost ?
ARITHMETICAL EXAMPLES. 89
114 . My farm consists of 8 fields,contain ing —5
l 6 "
9,22g, 1758, 152
3
6 ,and 1238 acres, respectively . H ow many
acre s in my farm_1_ _3
115. g3of 1
gQ of what number, dimin ished by ”7
,leaves
6
(4 8 ) 3 — 1q
(s r— 1
11 6 . My garden,which is 180 ft. long
,and 150 ft. w ide
,i s
surrounded by a tight-board fence 55ft. high . H ow muchw ill it cost , to paint the fence on both sides at per squareyard117 . Bought 3 7 T. 15cwt. 3 qr. 15 lb . of copperas, at
per lb. sold at one time 8 T. 12 cwt. 3 qr. 3 lb . at perlb. at another time 14 T. 3 cwt. 2 qr. 20 1b . at per lh. ;James Bond bought 5the remainder at per lb. and
John Gaines -5of what still remained at per lb .,George
Roo t,who bought the residue at 8.12 per lb .
,be coming a
bankrupt,paid but 50 cen ts on a do llar of his debt. What
was my whole gain ?118 . A farme r has 165bushe l s of corn, bushels of rye
,
5-76. bushe l s of wheat ; he w ishes to put the grain, w ithout
mixing,into the largest po ssible bags
,of equal size. R e
quired the number of bags,and the capacity of each.
119. A man bought 35 bushels of barley, and sold the
whole for 83 0 . H e made in the trade . What did hegive per bushel ?120. A tailor has 675yds. of cloth, from which he w ishes
to cut an equal number of coats, pan ts, and ve sts. Whatnumber of each can he out
,if they contain
,respective ly
,35,
yards ?12 1. From the annual report for 1863 , the to lls collected
on the canals o f New York for that year w ere as fo llows :On wood and lumber, 8715059 ; on an imals
, 888426 ; on
vegetable, 83 0 1282 3 ; on other fargn products, 814 114 ; on
manufacture s, 813 7107 ; ,
on merchandise, 813 7253 ; and on
90 ARITHMET ICAL EXAMPLES.
other articles enough to mak e the who le amount 84645207.
What was the amount colle cted on articles no t specified ?122 . How many bricks
,8 in . long
,4 in . w ide
,and 25in.
thick, are required to build the front of a house whose w all i s3 0 ft . long
,24 ft. high
,and 2 ft. thick
,allow ing the doors and
w indows to occupy 5the surface ?123 . A merchant purchased in Liverpoo l 3 4 bale s of clo th
for £8 19s . 5d. per bale ; he disposed of the cloth at ‘Ha
vana for 2 12 cwt. of sugar, at £1 58 . per cwt. What balance was due him in cash ?124 . A company of 3 6 persons purchased a trac t of land
contain ing 2766 A . 3 R . 12 P . J. Jenk s,who was one of the
company,and owned an equal share w ith the o thers
,sold 5of
his part for Is . 9d. 2 far. per sq. rd. What sum did hereceive125. H ow many silver dollars
,each we ighing 4 125grains,
could be made from the silver taken at the doors o f the greatLondon exhibition
,the weight of the Silver being 3 5English
tons ?126. During the last half of the year 1863 there were 189
fires in the city of New York,and the average loss by each
fire was 8223 8 40 ; the insurances amounted to 555times thelosses
,and the amount paid by the underwri ters was 83 83 07
.50 less than 5the amount of insurance. H ow much wasthe actual loss ?127 . What i s the value of a pile of wood that is 10 rods
long,4 feet w ide
,and 15yards high, at per cord
128. If a person spends in 6 months what he earns in 45months ; how many dollars can he lay by in a year, suppo sing he earns 83 25 in 25months ?
129. Aman has two kinds of flour ; the first is worthper barrel more than the second, and 9 barrels of the secondare worth as much as 7 of the first. W hat is the price of
each per barrel
ARITHMETICAL EXAMPLES . 91
13 1. The Connecticut river, which is 60 rd . 10 ft. w ide ata certain place
,has an average depth of 10 ft., and runs at the
rate of 35miles per hour. In what time w ill it discharge acubic mile of water ?13 2 . I f a man ’s property is worth 81500 , and he owes
81800 ; how many cents can he pay on the dollar ?13 3 . If a man can pay his creditors only 48 cents on a do]lar
,how much can he pay on a debt of13 4 . A boy
,having been sent to market to buy a certain
number of pounds of meat,found that if he bought beef at
105cents a pound, he would have 65cents remain ing ; but ifhe bought pork at 135cents a pound, he would lack 46 centsof having money enough to pay for it. H ow much moneyhad he ? and how many pounds was he directed to buy ?
135. A farmer w ishe s to build a b in 8 ft. long,6 ft. w ide
,
and high enough to hold 200 bushels of corn . H ow highmust he build it13 6 . H ow long from the Declaration of Independence
,July
4,1776
,to the firing upon Fort Sumter
,April 12
,1861
13 7 . The value of the products of Massachuse tts in 1860,
w ith a population of 123 1065,was 82893 00275 ; of Mary
land,w ith a population of 68703 4
, 865955264 . H ow muchmore per capita, was the value of the annual products of theformer than the latter State13 8. The total population of the Slave States in 1860 was
12229727 ; allowing the average annual products per head tohave been the same as in Maryland
,how much would the
value o f the products of the Southern States have been in
creased had the ratio of production been the same as in Massachusetts
13 9. H ow many bushels of coal w ill a boat 90 ft. long, 42
92 ARITHMETICAL EXAMPLES .
ft. w ide,and 55ft. deep contain , a bushel of coal being 1; on
feet ?140 . A person having 5of a hog
shead of w ine,so ld at one
time 5of a gallon, at another, 3 of a quart. H ow manygallons
,expre ssed decimally, did he sell, and how much
remained ?141. How many seconds has a person lived who is 3 2 yr.
197 da. old, allow ing for 8 leap years ?142 . Paid 3 debts successively
,each of which took 5the
money I had before paying it,and more ; after which I
had 825 remaining. H ow much had I at first ?143 . A man in Ohio bought .825of a firk in of butter atper pound ; .8575bushel s of corn at 8.0 15per pound ;
.7835bushels of wheat at per pound. What was theamount of his bill144 . What would be the expense of paper fo r a room 15
ft. 9 in . long,14 ft. 6 in . w ide, and 10 ft. 3 in . high
,which
contains 3 w indows,each 6 ft. 2 in . long, 3 ft. 10 in . w ide
,
and 2 doors,each 6 ft. 10 in . by 3 ft., a roll of paper being 8
yds. in length,and 5 yd. in w idth
,and costing
145. If I buy 120 gallons of rum fo r 875, how much watermust be added to i t that I may sell i t at 60 cents per gallon,and gain 815 in the sale of it ?146 . Of the poor people assisted by the State of New
York in 1863,486 were natives of Wale s ; 52 less than 4
times this number were Canadians ; and the Frenchmen were140 less than 3 times the same number ; the Scotch were 270more than the Canadians ; the English , 9 le ss than the sum
of the Welsh and twice the Scots ; the Germans w e re 190 lessthan 4 times the English ; and the Irish were 64 more thanthe sum of the W e lsh
,tw ice the Canadians and 55time s the
Germans ; the native born w ere 73 94 less than the Irish,and
the nationality of 2 1151 was unknown . Required the num
ber re l ie ved.
147 . The whole expense for the support of the poor for the
94 AR ITHMETICAL EXAMPLES.
se rved the Sabbath,and was allowed the Fourth of July and
Thanksgiving as holidays ?159. What is the amount of the following bill
CLE VE LAND,Jan . 1
,1864.
M R . PETE R J ONE S
B ought of SAM U E L CARTE R 61. Co.20 lb . Rio Coffee 8 .40
3 5'
w . India Sugar e 16524 Pearl Starch 14
6 gal . Molasses °75
75 lb . Cream Crackers 1 1
20 Soda .105
160 . So ld 125 equal loads of wood,measuring 1 15Cd. 3
ed. ft. 7 cu . ft. for What is the quantity per load,
and price per co rd ?161 . Bought 14 lots of land
,each contammg 3 7 P . 200 sq .
ft. ; from this purchase I so ld 2 A . 2 R . 25P . 60 sq. ft., and
the remainder I disposed of at 2 s. 35d. per sq. ft. H ow muchdid I receive for the last sale ?162 . What is the value of 71963 0 pounds ofwheat atper bushel ?
163 . H ow many half-dimes would it take to pay for 18
doz. of eggs,at per doz .
164 . A farmer,having harvested his crops
,finds that he has
corn enough to fill the first of the fo llow ing boxes ; wheatenough to fill the second
,and rye enough to fill the third.
The outer dimensions of the boxes are as follows : of the first,
105ft. long, 65ft . w ide and 6 ft. high ; of the second, 95ft.long
,75ft . w ide and 55ft. high ; of the third, 12 ft. long, 10
ft. w ide and 7 ft. high ; they are made o f plank 2 in . thick .
H e se lls the corn at 5 a bushel,the wheat at the
rye at H owmany bushels of cu . in . had he of eachkind of grain
,and how much money did the whole bring him ?
165. A man has a fie ld 3 75rods w ide. W hat length musthe cut off from the end to se t off 5A . 3 R . 25P . ?
ARITHMET ICAL EXAMPLES . 95
166. The Mississippi River flows dire ctly south, through19
°
15'of latitude. The earth is an oblate sphero id
,and the
equatorial diame te r i s 13 miles more than the polar diameter.H ow much farther from the centre of the earth is the mouthof the river than its source ?167 . The above river, on account of its numerous w indings,
is 3 160 mile s long. What is the average rise of the river permile ?168 . If the factors o f a certain number are 165, 3 0 37 and
9395 ; what is 15of ],3 of5of the number ?169. Jo sephus relates that the battering ram employed by
Titus against the walls of Jerusalemw e ighed 100000 poun ds .Now if his men could move i t w ith a velocity o f 6 ft. a sec
ond,how many cannon balls of 100 pounds each
,discharged
w ith a ve locity of 1200 ft. a second, would b e necessary tostrike the walls w i th equal force ?170 . H ow many francs must a merchant in Paris send to
New York in payment for a debt of 815989 862 ?17 1 . I have a fie ld 96 rods long and 50 rods w ide . H ow
much would it cost to build a fence around it,at per
foo t ?172 . Reduce .18
,.369
,.307692 and to equivalent
common fractions.173 . Gen . M cClellan estimated the rebe l forces engaged in
the battle of Antie tam as fo llow s : Gen . Jackson ’s corps,24
778 men ; Gen . Longstr ee t’s,143 6 le ss than Gen . Jackson ’s ;
Gen . Hill’s,15525; Gen . Stuart’s cavalry
,6400 ; Gen . Jen
kins’,200 more than 5of Gen . Stuart’s re serve s
,18400
,and
artillery 400 guns,w ith 15 men each . What was the esti
mate of the rebe l force ?174 . The Un ion army in the same battle numbered as fol
lows : l st corps,14856 ; 2d corps, 18813 ; 5th and 6th corps,
126 15 men each ; 9th corps, 13 819 ; 12 th corps, 3 693 lessthan the 9th ; and the cavalry 1 15more than 5the 5th corps.What was the strength of the Un ion army
96 AR ITHM ETICAL EXAMPLE S.
175. If a man fill 5of a cask w i th brandy, 5w ith w ine,and5w ith wate r, and i t lack 2 15gallons of being full , howmany gallons w ill that cask contain ?176 . A man , having 55of 5 tons of iron, sold 5of 9 cwt.
W hat was the value of the remainder at 125 cents perpound ?177 . Light moves 192000 miles per second ; sound, 1142
feet per second, and a cannon ball , w ith an average velocityof 800 feet per second . If a ball is discharged from a cannon 6 miles distant from a person
,how long after the flash
is seen w ill the sound reach his ear, and how long after thesound w ill the ball arrive ?178 . The average distance of the planet Neptune from the
earth is 2864000000 miles ; should i t be blotted out, howlong thereafter would its l ight b e vi sible from the earth
,the
velocity of light be ing 192000 miles per second ?179. Exchanged 5firk ins of butter of 50 lb . each
,at $755
per pound,for 50 bags of guano
,of 1 165lb. each. W hat
was the price of the guano per short ton ?180 . What w e ight of water in a cistern 10 ft. 6 in . square,
and 8 ft. 4 in . deep,a cubic foot of water weighing 1000
ounces ?181. Great Britain
,w ith a population of 293 3 4788, had in
1861 a national de bt of $3 917945913 , the annual interest ofwhich was W hat was the average deb t andannual interest to each person182 . France
,w i th a population estimated at 3 6000000 , had
at the same time a debt of $2206000000, the annual intere sto f which was $110000000 . W hat was the average debt andin terest to each person ?183 . What w ill i t cost to construct 8 mi. 6 fur. 16 rd. of
plank road at per mile ?184. W hat part of a short ton i s 5of a long ton185. H ow much copper and tin in the great hell of M os
98‘ARITHMETICAL EXAMPLES .
so ld the same at 10 cents per pound. H ow much was hisgain ?196 . F. F. Smith has coffee at $ 3 75, per pound cash, but
in trading w i th Se th Bishop, he charge s $ 42 . What- .mustB ishop charge him
'
for potatoe s that he sells at $ 625cash ?197 . On 5of my fie ld I raise tobacco ; on 5of the remain
der I sow oats ; po tato e s are planted on 5of what still re
mains,and carrots on 5of the re sidue I have left two small
piece s,one of which is 4 rods square, and the other contains
4 square rods. H ow large is my fie ld ?198. There were 44192 16 bale s of cotton , each 400 lbs.,
expo rted from the Un ited States in 1860 , at an average priceo f $ 108 per pound , and 167248 hogsheads of tobacco at
per hogshead. What was the value of co tton and
tobacco expo rted ?199. If by selling clo th at 105. 6d.
, 5of the price i s gain ,
what part of the cost would b e gained by se ll ing i t at 13 shilhngs ?
200 . From 10 years subtract 9 yr. 9 mo . 9 wk . 9 da . 9 h.9 min . 9 sec.201 . A merchan t bought 15 barrels of salt
,of 4 bushels
each,at $15a barrel , and re tailed i t at 5of a cent a pint.
H ow much was his who le gain202 . The Pennsylvan ia Central Railroad is 3 56 miles long
4 passenger trains and six fre ight trains pass over i t bothways each day of the year, Sundays excepted. H ow manymile s do the trains run each year ? and how many times thecircumfe rence of the earth
,which is about 25000 mile s ?
203 . A ship’s chronome ter,set at Greenwich
,points to 5h .
45 min . 24 sec. P . M ., when the sun i s on the meridian.
What is the ship’s longitude204 . Bought A . ( f land at
515 of £2 l 1s . 6d.
,New
England currency, per square rod . H ow many dollars did itcost ?
A RITHMETICAL EXAMPLES. 99
205. The salary o f the President of the Un ited States is$25000 per annum. H ow much can he spend each w e ek
,
and ye t save $27200 in one term of o ffice ?206 . Required the quotients of 1169 divided by its twopr ime factors next larger than 1 .
207. A farmer bought some oxen,cow s
,and sheep for
$1860 , paying $45, $ 25, and $4 per head, respectively.
There were 5 time s as many cow s as oxen,and 7 time s as
many she ep as cows. H ow many of each did he purchase208. A owns
355o f a fie ld
,and B the remainder ; 5of the
difference be twe en the ir share s is 5A . 3 R . 165P . What isB ’s share ?209. The average fall o f rain at Wo rcester
,Mass
,i s
in . of snow in . allow ing 5 in . o f snow to make one o f
rain,how many hogsheads of water fall annually upon a flat
roof 40 ft. long by 3 0 w ide ?2 10 . A w ine merchant w ished tw ice as many quart bottlesas pint ; tw ice as many pint as halfipint, and tw ice as manyhalfipint as gill bottle s filled from a cask o f w ine contain ing58 gal . 1 qt. l pt. 2 gi. H ow many bottles of each kindcould he fill2 11 . Pe ter Jones was born Sept. 7 , 183 0 ; he was 27 yr.
3 mo . 2 3 da. old when married ; and 3 yr. 2 1 da. after marriage his first child was born . What was the date of his marriage ? and what his child’s birth-day2 12 . H ow much more is the co st of 3 9 A. 2 R. 15P . of
land at per acre, than the expense of making 5mi. 6fur. 24 rd . of road at per mile ?2 13 . There were shipped over the Erie Canal in 1863
1603 065barrel s of flour,223 3 643 3 bushels of wheat, 19918
464 bushels o f corn,and 3 816548 bushe ls o f barley ; the toll
fo r the flour was $ 3 75per barrel , and for the grain $ 075perb ushel ; oats were shipped in such a quantity that the to ll sfrom the oats
,barley
,and corn we re equal to the to lls
100 ARITHMETICAL EXAMPLES.
from the flour and wheat. H ow many bushe l s of cats w ereshipped ?2 14 . Two boys purchased a pair of skate s in company ;
one paid $5, and the other $155 ; they so ld them so as to
gain $775. What did they se ll them for and how much waseach one ’s share of the gain ?2 15. H ow lo ng befo re the vo ting is ended in San Francis
co,Lon . 122
°
13’
W .,can the voters of Eastport
,M e .
,Lon .
670
W ., te legraph to San Francisco the result of their e lection ,
the po ll s clo sing in bo th places at sunse t ?2 16 . At what time be tween 11 and 12 o
’clo ck is the minute-hand as far beyond the XI as the hour-hand lacks of be ingup to the XIImark2 17 . A man started from Portland
,Maine
,w ith $100 ; he
paid for his fare to Bo ston ; in that city he bought abook for 5s . 6d.
,paid 8s . 3 d. hote l bill and 3 8 . 3 d. for amuse
ments ; he then took passage in a steamer for Charleston,
S. C.,paying $3 2 ; in that city he purchased 8 yards of cloth at
13 s . 6d. per yard, and paid 18s . 9d. for having the cloth madeup ; he then w ent to Philadelphia, at an expense of $25, andthere he purcha sed some pictures for 15s . 11d.
,some pre sents
for 18s . 5d.
,and spen t 17 s . 8d. at a hotel ; the Camden and
Amboy Railroad Company agreed to carry him to New Yorkfor the rest of his money the regular fare be ing how
much did the company lose ?2 18 . At $1000 per acre , what is the value of a strip of land
44 yards long and 20 f e et w ide ?2 19. The value of exports from the Un ited States- in 186 1
,
was as fo llows : the products of the sea, $4451515; of the
fo rest, $10260809 o f agriculture
, $1 0 165583 3 ; tobacco ,$13 7847 10 ; co tton , $3 4051483 ; manufacture s, $3 64 18254 ;raw produce , $3543 695 specie and bull ion , $23 799870 .
H ow much did the expe rts of the products of agriculture andmanufacture exceed all o thers in value ?220 .
The hour andminute hands of a clock be ing together
102 AR ITHMETICAL EXAMPLES .
the we ight of water in a cistern contain ing 500 cu . ft. 864cu. in . ?
229. What are the values of a bushe l of peas,sold at 10
cents a quart,by w ine
,beer and dry measure
,re spectively
2 3 0 . The total lo ss o f the Federal army in the battle o f
Fair Oaks was 573 9 ; the priso ners were 3 3 2 more than thekilled
,and the wounded were 459 more than 15times both
the killed and prisoners. What were the various lo sses ?23 1 . What is the cost of a great gross of pens
,at 65cents
for 5of a dozen ?2 3 2 . A person desirous of giving 1s . 6d. apiece to some needy
boys,found that he had no t money enough in his pocke t by
5d. ; he therefore gave them each 1s . 4d.,and had 9d. left.
Required the number of boys.23 3 . A housew ife exchanged old Si lver for a feather bed
worth $24 ; the feathers were valued at $ 80 a pound, andthe silver at 25 times the value of its own weight of feathers.W hat was the Troy weight of the silver ?23 4.
If a man can paint 4 sq. yd. in one hour, and i s 3 1 h .
6 mi n . 40 sec. in painting two sides of a wall 7 feet high, howlong is the wall2 35.
The earth moves through 59 .14' daily, how far did it
move during the month of February, 1864 ?
23 6 . The average cost of the school house s in Ohio, in1861
,was The total cost of the same was $4794Required the number.
2 3 7 .The value of the common school libraries at the same
Sime was the books were worth on an averageeach
,and were distributed in l ibrarie s averaging 47
7ols . each . Required the number of l ibraries.23 8 . In the same state 27 106 teachers w ere examined dur
ing: the year 186 1 three times the number rejected were 93 4
mo re than the numbe r conside red qualified to teach. H ow
many passed examination , and how many were rejected ?
AR ITHM ETICAL EXAMPLES. 103
2 3 9. A person bought a watch, chain andpencil , for £3 0 the
chain cost tw ice as much as the pencil,and the watch tw ice
as much as the chain and pencil . What did he give for each ?240 . If I exchange 4 bu . 15pk . of po tatoe s for 2 bu. 2 pk .
of apple s ; how many bushels of apple s ought I to rece ive inexchange for 3 3 bu. 1 pk . of potatoes at the same rate241. Aman chopping wood at 5per co rd, earnedduring the wo rking days of January
,1864
,and was idle 2 ‘
days. How much wood did he cut, on an average, per day ?242 . A boy having been sent to the store w i th 55doz . ofeggs
,was directed to purchase w ith them equal quantitie s of
sugar,coffe e
,butter and tea ; he d ispo sed o f his eggs at the
rate of 2 for 5 cen ts, and paid for the article s purchased 17 ,28
,3 75and 13 75 cents per pound respectively. What
amoun t of each did he purchase ?243 . A bowlder, containing 5of 5o f 235cu. ft. , i s what
fraction of a perch ?244 . A grocer bought 10 bushels of beans at $3 per bushe l,
and ordered his shop boy to retail them at 15 cents a quart.By mistake the boy used a w ine quart. H owmuchmore wasthe groce r’s gain than he expected ?245. What part of 12 yd . 1 ft. 6 in . is 5511-5 of a mile ?246. Four men receive for hauling coal ; the firsthauled 2 T. 3 cwt. 3 qr. 18 lb. the second, 5T. 16 cwt. 7 lh. ;
the third,4 T.,
18 cwt. 2 qr. ; the fourth, 14 cwt. 20 lb.
H ow must the money be divided ?247 What is the difference in weight between 8 lb . of gold
and 8 1h. of lead248 . A speculator purchased bushels of corn in
Chicago,at 5s . 6d. per bushel, and so ld one-half o f it in New
Jersey at 8s . 4d. per bushel , and the other half in New Yo rkat 9s. 6d. pe r bushel ; the freight was $ 10 a bushel, and o thercharge s amounted to $23 0 . The corn being bought and so l dby we ight, how much did he gain
104 AR ITHMETICAL EXAMPLES .
249. My garden i s 105rods long, and 85rods w ide , andsurrounded by a fence 75fe e t high ; I have laid out a walkaround it
,w i thin the fence , 75fe e t w ide on the two side s, and
55fe et w ide on the ends . H ow much remains for cultivation250 . What part of a cord of wood is a load 75ft. long, 25
ft. high,35ft. w ide ?
251 . It is estimated that England use s annually,1000000
pounds of ivory . The average product of ivory from eache l ephant is 120 lb . ; and for every 25 e lephants captured 12men are killed . Required the number o fmen killed annuallyin hunting the e lephants that supply England w i th ivory ?252 . H ow many do llars
,Canada currency
,are equal to
$150 Un ited State s currency ?253 . If 535 of an acre produce 28 bushe ls of potatoes
,how
many bushe ls w ill 4 acre s produce,at the same rate ?
254 . Bought 78 A . 3 R . 15P . 7 sq. yd . 5 sq. ft . 9 sq . in .,
at $80 per acre ; I so ld 5of i t to A ,at $120 per acre ; 5of
the remainder to B,at per square rod ; and the residue
to C,at $ 005per square foo t. H ow much did I gain ?
255. H ow thick is a cubic inch of go ld,beaten so as to cov e r
a space 83 ft. 4 in . long and and 2 3 ft. 5 in .~ w ide
256 . During 1861, the Dead Le tter Po st Office sen t outfor de l ive ry 10580 money le tters
,and 1023 5 le tters contain
ing other articles of value ; 8998 of the former and 9552 ofthe latter were del ivered ; 12 14 money letters and 475othersw ere re tur ned
,unclaimed and no thing was heard from the
rest. H ow many were unreported ?257 . The money le tters contained of which $46
was del ivered,and was returned ; of the re
mainder,
belonged in the loyal State s,and the rest in
the disloyal . What amount belonged in the rebe l States3258 . At $3 8 75per square, what w ill be the expense of
floor ing a house in which there are 4 rooms,14 ft. 6 in. by 15
106 ARITHMETICAL EXAMPLES .
the same mile -stone at an interval of 5 hours . H ow long andhow far must the second travel
,after passing the mile -stone
,
to overtake the first269. What is the length of the shorte st piece of clo th from
which a number of garments can be cut,w ithout waste
,con
tain ing a yard,an ell Flemish
,an ell English
,and an ell
French,re spective ly ?
270 . The shadow of a cloud was observed to move 600 ft.in 235sec. W hat was the W ind ’s ve locity per hour ?271. From 183 8 to 1863
,3 858 patients w ere admitted into
the Central Lunatic Asylum,Ohio ; o f the se
,2000 were dis
charged as fully recovered,4 12 as improved
,724 as incurable ,
and 470 died . H ow many remained in the asylum,Jan . 1
,
1863 ?
272 . A gentleman bought 95 yards o f clo th, 5of a yard
w ide,for $100 , and gave the same and $25 for cloth of the
same quality,1 yard w ide . H ow many yards did he buy ?
273 . If a ve sse l sail 80 league s in a day, how many statutemile s do e s she sail274 . A farme r exchanged 11
. loads of potatoe s, each loadcontain ing 12 barrels of 25bushe l s each
,at $ 50 per bushe l,
for a number of piece s of clo th,each contain ing 12 yards,
worth per yard . H ow many piece s did he rece ive ?275. How many fe e t of boards w ill i t require to inclo se abarn 40 ft. 6 in . long
,3 0 ft. 10 in . w ide , 18 ft. 4 in . high, and
each side o f the ro of 16 ft.,allow ing 3 85ft. 3 in . for the gable s
276 . What is the value o f .05751953 125Cong.
277 . A degre e o f longitude,in the latitude of Bo ston ,
measure s 445geographic'
mile s . H ow many more statutemile s in 10 ° of longitude at the equator than in the latitudeo f Boston278 .
Rhode Island in 1862 expended $1683 65 in educating27750 children . W hat was the average expense per child ?
279. In the same year Ohio spen t 511283 4066 for the educa
AR ITHM ETICAL EXAMPLES. 107
tion of 7 17726 children. How much more did Rhode Islandexpend per child than Ohio ?280 . Massachuse tts
,during the same period
,paid out
$16 12824 for the instruction o f 2200 10 children.
“
H ow muchdid the ave rage expense per child in Massachuse tts lack of
being tw ice the expense incurred by Ohio for each child ?281. H ow many inche s higher is a horse that measures
165hands than one that s tands 145hands high282 . A person
,dying
,left in cash $6250 , and 4 house s,
Valued at each ; his indebtedness wasand he left directions that $100 should b e expended fo r amonument ; the residue was to be divided among his 4sons
,so that each should rece ive 5as much as his next o lder
brother. Required the share o f each.283 . If the re are 3 1181 verse s in the Bible and a personreads 88 ve rse s on Sunday
,how many must he read each
week-day to comple te it in a common year ?284 . A tract of land measuring 4059 A. 2 R. 16 P . was
divided among a regiment of men,consist ing of one colonel
,
1 major,6 captains
,8 l ieutenants
,24 sergeants
,and 220
private s,so that a private had one share
,a sergeant tw ice as
much,a lieutenan t 6 share s
,a captain 8
,the major 14
,and
the co lone l 20 share s. Required the share of each ?285. From the sum o f 5lb . 2 5
5.
—5oz. 155pwt, take the diff
fe rence b e twe en 5o z . and 5pwt.
286 . The earn ings of the To ledo andWabash Railroad Company in 1862 w ere $13 74517 , which was 55of the earn ingsin 1863 ; the expenses each year w ere $4772 1 more thanhalf the earn ings in 1863 . H ow much more were the net
earn ings of 1863 than of 1862
287 . What is the least number,which
,be ing divided by
3,5,7,9,and 10
,leave s a remainde r of one ?
288. What part of a hogshead of w ine i s 3 gal . 1 qt. 2125gills
108 AR ITHM ETICAL EXAMPLES .
289. A
‘
speculator in New York bought 1000 bushe l s ofgrain at per bushe l , and shipped the same to England,paying '
$125 transportation ; he sold the grain at per
Imperial b'ushel . What was his gain290 . I f the diamete r of the sun b e 884000 mile s
,and that
of the earth 8000 mile s,how many bodie s of the size of the
earth,placed m a l ine
,would reach across the sun’s diame ter ?
291 . Reduce 6 leagues, 2 mi. 3 fur. 17 rd. 4 ft. in . tostatute mile s.292 . The Austrian empire contain s 7889925 Germans
,
15027646 Slavi , 563 2689 Rouman ians, 4947 13 4 Magyars,and of other races a number making the entire population3 47 143 26 . H ow many belong to national ities notmentioned293 . Paid in t e ndon £1955fo r 12 bales of cloth . H ow
many bales should be received for294 . A farmer sold 8 leads o f potato e s
,averaging 27 bu .
3 pk . 5qt. each , fo r $ 45 a bushe l . H ow much did he re
ce ive
295. D ivide among A,B and C
,so that B may
have less than A,and more than C.
296 . If the population of the world b e as follow s,viz
Asia,63 0700000 ; Europe, 2654943 00 ; Africa, 6 1700000 ;
America,57600000 ; Ocean ica, 23 400000 ; and the ave rage
length of l ife be 3 3 —3 years,what 13 the average number of
deaths each day ?297 . H ow many mo re bushe l s w ill a cubical box co ntain,
whose sides measure 8 ft .,than one that i s 10 ft. long, 8 ft .
w ide,and 6 ft. de ep ?
298 . H ow many seconds in 40 tropical years, 3 40 da. 22 h.
3 7 min . 45 sec.?
299. A surveyor,measuring a piece of land in the form o f
a r ectangle,found one side to be 55 ch . 50 l., and the other,
63 ch . 24 1. H ow many acre s did it con tain ?3 00 . In Ohio there al e 997 miles of canals, the aggregate
110 AR ITHM ETICAL EXAMPLES .
3 10 . A merchant bought 150 gallons of molasses at $ 60 agallon, and intended to have it sold at $ 75 a gallon , but hisclerk, by mistake, sold half of it by beer measure at $ 15 aquart ; discovering the blunder he directed him to sell the remainder at $ 18 a quart, w ine measure. H ow much morethan the cost did he re ce ive for the molasse s ?3 11. A meteorological observer
,in Cayuga Co unty
,New
York , registered the total fall of rain , in 1861,of in . ;
of snow,in.
,and in . of snow made one inch o f
water. H ow many hogsheads of water fe ll,during the year
,
in the town of Genoa,which is 10 mile s square ?
3 12 . The whole length of railroads in the United State sJan . 1
,1852
,was 10900 mi les ; ten years afte r, the number
of miles open for traffic was 23 le ss than 3 51 times this number ofmiles ; the total cost of the roads and equipments, atthe last period mentioned
,was $1 192400424 . What was the
average cost per mile in 1862 ?3 13 . H ow many pipes of Port are equal to 2 3 o f Sherry ?3 14 . I f there are grains of pure silver in one do llar
,
how many silver do llars are equivalent in value to lb . . of
English standard gold ?3 15. What cost 4 bundles, 1 ream,
6 quire s,12 she e ts of
paper at per bundle ?3 16 . The Austrian army, in 1863 , was composed of 1603 16active infantry ; 424000 re serve ; the active cavalry was 5the active infantry, le ss 2 35; the reserve cavalry, 2490 lessthan 5the re serve infantry ; all othe r activé troops, 5674more than the active cavalry ; and all o thé r re serve tr0 0 psw ere 169 less than all the} cavalry ; the population be ing3 47143 26
,what proportion of the people were soldiers ?
3 17 . Gunpowder made acco rding to the governmen t rece ipt, is a compound of 5n itre
,and equal parts of sulphur
and charcoal . H ow much of each in 1.
ton o f powder ?3 18 . H ow many cubic quarte r inche s in a slab of marble
2 yd . long,1 ft. 6 in . w ide
,3 in. thick ?
AR ITHM ETICAL EXAMPL E S . 111
3 19. A ship captain,sailing from London to New Yo rk
,
found,on taking an obs ervation
,that the sun at no on was 3 h .
25min . 40 see . later than the London time,as shown by his
chronome ter. H ow many degrees we st had he sailed ?3 20 . In 1855 the U . S. Go vernment sold 15729524 acres
of public lands,for H ow much did John
Smith pay for a quarter section,at the average price per acre ?
3 2 1. A farmer planted a field,3 0 rods long and 20 rods
w ide,w ith corn ; the hills were in squares, 3 fee t apart, and
the outside rows 1 ft. 6 in . from the fence ; allow ing each hillto produce 5 cars
,and 8 ears to make a quart
,how much was
the corn raised on the field worth at $ 80 a bushe l ?3 22 . The five different race s number as fo llow s : American,
1 1000000 ; Malay, tw ice as many 1500000 ; Ethiopian,
3 0000000 more than the Malays ; Caucassian , 5 the who lepopulation o f the earth— 19400000 ; and the Mongo l ians
,
450800000 . H ow many more Caucass ians than Mo ngolians,
and what is the to tal population o f the earth ?3 23 . If the longitude of Bo ston i s 70 o 4 ’ We st
,what w il l
b e the time in that place when i t is 3 h . 35min . A . M . in
London3 24. Albert Tucker, own ing 80 acre s of land, cultivated 15acres potatoes
,35corn, 25rye , 15oats, 5carro ts, 5turn ips ,
from which he harve sted 160 bushels po tato e s,485corn , 28
rye , 56 oats, 650 carro ts, and 720 turn ips per acre , re spectively. H e cut 15tons hay on each of 125acre s, and uponthe remainde r he pastured 3 0 she ep, 5 cows
,2 ho rse s and 8
ste ers,fo r 24 we eks. H e so ld his po tato e s
,co rn
,rye , oats ,
carrots and turn ips at $ 75, $ 40 , $ 25and $ 15
per bushe l , re spective ly he sold his hay at $16 per te n , andreceived 3
,20
,45and 15 cents each per w e ek
,re spective ly
,
for pasturing the she ep,cow s
,horse s and ste e rs . What were
the ne t profi ts of the farm,suppo sing he paid $25 taxe s, and
$3 0 , $28, $16, $16, $40 , $3 2 and $5 per acre , re spective ly,f or cultivating and harvesting tha po tato e s, co rn, rye , oats,carrots
,turn ips and hay
CHAPTER V .
1 . My salary is $800 a year. I pay 357; of i t for board ,1 1% for clo thing, 1275 for books, and 7% for incidentals .H ow much are my yearly e xpe nses ?2 . If 135bushe ls of whe at make 3 barre l s o f flo ur
,how
many bushels o f wheat w i ll b e require d to make 40 barre lsof flour ?3 . A farmer raised 20% more o f woo l this year than last ;the amoun t raised during the two years was 13 20 lbs. \Vhat
amoun t of wool was raise d each ye ar ?4 . A horse which cost me $13 5 I so ld for $150, on 9
months’ credit. H owmuch did I gain,money being worth5. The debt created by the U. S. Government fromMarch
7,186 1
,to July 1
,1862
,was $451456866 ; $125090 mo re
than of this pe rtained to civil affairs ; the remainde r wascaused by the war. H ow much did the rebell ion expense save rage per day ?6 . I purchased 6000 bushe ls of wheat in Chicago at
and shipped the same to my agen t in Albany, who so ld i t at$16 25. H ow much did I make
,after paying $543 fo r e x
pense s and a commission of 25757 . A man sle eps 75hours each day. \Vhat pe r cent. of
his time do e s he sle ep ?8 . The amoun t o f mo ney deposited in the sav ings banks
o f New York,in 1863
,was $54557500 ; the amo unt w ith
drawn from the same during the year was $113 47960 .
What per cent. of the amount depo s ited was w i thdrawn , andhow much was the annual intere s t at 5% on the money re
main ing9. If 24 men
,in 9 days o f 12 hours each, build a wal l 200
1 14 AR ITHM ETICAL EXAMPLE S.
19. The expenses of a schoo l for one year were $2000 forsalary of teachers
,for fuel
,fo r incide ntals ;
the public money was and the remainder was paidby a rate bill. If the aggregate attendance was 35275 days
,
how much must John Spencer pay, who sent 3 pupils 175days each20. Sold g. of a hhd . of molasses for what the whole cost
me . W hat was my gain per cent.2 1. W hen does the amount of the follow ing bill becomedue
,per average ?GE ORGE BAR BOUR
,
1864. To J. B . HALE D r.
Jan. 20 To 100 yd . Broadcloth25 2500 Shee ting 12
March 20 3 000 M errimac Prints 18
April 1 3 00 French Silk 5
22 . If a man , by laboring 12 hours e ach day, can pe rforma piece of work in 3 weeks
,by laboring 6 days in a w e ek
,
how long would it take him to do the same,i f he labor 10
hours each day ?23 . Bought 4 hhd . of sugar, each con tain ing 1825 lbs . , at
65cents per pound, and paid fo r fre ight,sto rage and
cartage. Allowmg 570 for leakage and waste , fo r how muchper pound must I sell the remainder to gain24. Bought a house for $4500 , and paid $500 cash ; the balance is to be paid in 8 equal annual installments . W hat isthe mean time for paying the balance ?25. W hat is the difference between the in terest and discount of for 1 yr. 4 mo .
,at
26 . So ld a horse at gain,and w i th the money bought
another horse , which I sold for $120 , and lo st D id I
gain or lose by my trading ? and how much ?
27. An insurance agent, whose commission was 1055on all
AR ITHM ETICAL EXAMPLES . 115
sums rece ived for the company, cleared in one year.W hat were the company ’s ne t rece ipts from the agent
28 . In 1862 the cavalry in the French army w e re 1921, 0
Of the infantry ; the artillery were 66% o f the cavalry ; thee ngineers were 22 ‘
rsr% of the artillery and the gens-d ’arme s
.3 9 of the artillery . If the engineer corps numbered 15000men
,what was the strength of each of the othe r arms
29. The Financial Committee Of a graded school invested$3 3 90 1 . in U. S. 7
77} Treasury Notes, which w ere at a premium of 45356, as a fund for the support of the school ; the sal
aries of te ache rs amounted to $1975, and was paidfor incidentals. What sum was annually left unexpended ?3 0 . If 12 boarders eat $25worth of bread in 2 mo .
,when
flour is per barre l , in how many months w il l 15 boarders eat $60 worth of bread, when flour is $12 per barre l
3 1. A shipment of wheat was insured at to cover 2 ofi ts value ; the premium paid was the wheat be ingworth $8 0 per bushe l, how many bushels w ere shipped ?
3 2 . Which is the more profitable to buy 7 ’S at or 5
’s
at 80%3 3 . The cash capital o f the West Roxbury Horse RailroadCompany is $40400 ; the net receipts for one year were$3 3 12 . If of the ne t receipts b e re served in favo r o f theCompany
,how large a dividend may be declared ?
3 4 . A,who i s worth $6845, i s tax ed what is B
worth,who is taxed
35. J . BURNS in accoun t withTYLE R Co.
1860.
Feb . 25 To M dse . on 3 me . 3 60March 20 u u 3 | 240Apn l 26 3 875
J une 24 $ 6 $5 65 2 H 235
Required the cash value of,the above account, July 1, 1860 ,interest at
116 AR ITHM ETICAL EXAMPLES.
3 6. The loans and discounts of all the banks of Philadelphia amounted to $29705200, Oct . 19, 186 1 ; the specie invaults was $63 75750 ; the deposits $2 1100085 and the
capital stock paid in, $118 1 l500 . On the' first o f Jan.
,1863
,
the loans and discounts had increased per cent. ; the
specie had diminished 295pe r cent . ; the deposits were 285more ; and the capital stock paid in
, go f one per cent. le ssthan in Oct. 1861 : loans
,discounts
,and spe cie being re
source s ; deposits and capital stock be ing l iab il ities, how muchwere the resources in excess of the liabil i tie s
,Jan . 1
,1863 ?
3 7 . A stack of hay w il l keep M cows or 18 horses onew eek . H ow many days w ill i t keep 5 cow s and 5 ho rses ?
3 8. A merchant pays $10050 fo r a stock of goods ; he se ll sthem at an advance of the expenses conne cted w i th thebusiness are $1750 . H ow much does he gain ?
3 9. The value of real estate and pe rsonal property in Kentucky in 1850 was $3 0 1628456 ; in 1860 i t was $666043 112 .
What was the increase per cent. in 10 years ?
40 . The value of real estate and personal property in Ill inOis in 1850 was $1562655006 ; in 1860 , $87 1860282 . WhatWas the increase per cent. in 10 years ? H ow many time sas great was the increase of property in Illinois than in Kentucky
41 . $1200 77
ofio
BOSTON, Feb . 1. 1863 .
Six months after date I promi se to pay Know les,Leland
,(St or order
,twelve hundred and 1
766
6do llars
,w ith
in tere st,for value re ceived .
S. M . SM ITH .
Indorsed as fo llows : April 16, 1863 , Aug. 1,
1863,
D ec. 16 , 1863 ,H ow much was
due April 1 , 1864 ?
42 .A farmer bought 100 o xen , cow s, and she ep for $1 160 ;
there were 6 time s as many cows as oxen , and 3 time s asmany sheep as cows ; the oxen cost tw ice as much per head,
ARITHMETICAL EXAMPLES.
$2520 ; allowing 4% for collecting, for what summust thetax b e levied ?52 . A merchant tailor bought 4 pieces of cloth
,each con
tain ing 3 0 yd . qr.,at per yd . he sold f; of it at
per yard , and made up the remainder into suits, eachcontaining 7 yd . 2 qr.
,which he sold fo r each . H ow
much did he gain53 . W hat sum must I inves t in United States 6’
s,selling
at 21, premium,to se cure an annual income of $840 ?
54. What is the rate of income upon money invested in6 per cent. bonds
,purchased at a discount of 10 pe r cent. ?
55. If it require 192 reams of paper to print 2400 copiesof an 8vo book
,contain ing 440 page s
,how many reams w ill
be required to print 6000 copies of a 16mo book,containing
220 pages56 . Goodman andBarbour bought bills of goods ofMe ll en
,
Claflin,and Co .
,New York
,as fo llows
,viz. : Jan . 1
,1863
,
$750 ; June 1,1863
, $1250 ; Sept. 16, $2525; D ec. 3 1
,
1863,
they bought on time,paying legal in terest.
What was the ir whole indebtedness,May 1
,1864 ?
57 . What must I pay for U. S. 6 per cents,that the invest
ment may yie ld 8 per cent.58. A man
,dying
,left $3 565 to be placed at intere st fo r
his son,who was 16 yr. 5mo . 15 da. old ; how much w ill he
re ceive when he is 2 1 years old , allowing 7% inte rest ?59. The population ofNew York city, in 1860, was 805650 ;
it was estimated to have increase d 20 per cen t. Jan. 1,1864.
Suppose at this last date the whole population were drawnup in single fi le
,each person occupy ing a space of 25ft.
,and
the whole l ine Should begin to march at the rate of 2} mile spe r hour, what would be the length of the l ine, and how longwo uld the procession be in passing any given po int ?60. A house being rented for $12 a month pays 75percent. interest, what i s the .value of the house ?
‘
ARITHM ETIOAL EXAMPLES 119
61. Bought 5000 bushe ls of wheat on 6 months’ credit, atI immediate ly so ld it at cash
,and put out the
money at 675 ; at the end of 6 mon ths I paid for the wheat.Did I gain or lo se by the transaction
,and how much ?
62 . Thomas Bake r bought a farm fo r $20000 cash, o r
$10000 payable in 6 months, and $12000 in 1 yr. 6 mo . he
cho se the latte r mode of payment. Money be ing worth 7%did he gain o r lo se
,and how much ?
63 . The earnings of the Chicago and Northw estern R. R.
fo r the w e ek ending Jan . 14,1864
,w ere more than
for the same per iod in 1863 ; the earn ings for the w e ek men
tioned,in 1864
,be ing an increase of 48% ove r the earn ings
o f the corre sponding w eek of the previous year,what we re
the earn ings fo r the week in 1864 ?64. A’s money is 50% more than B’s . H ow many percent. le ss is B ’s than A’s ?65. Bought 450 barre l s of flour at which I paid fo r
in’ iron at 3 cts . pe r pound ; the purchaser Of the i ron afte r
wards so ld of i t to a scythe manufacturer. What quan titydid he sell66 . What is the difference be tween the simple and com
pound intere st of $700 in 3 years at 5 pe r cen t . per an
num
67 Reduce 9 sq. rd.
‘
9 sq . yd . 7 sq. ft . 120 sq. i n . to thede cimal of of gof
'
gof 3 5A . 2R .
68 . A man dying le ft of his property to his w ife ;50% of the remainder to his son ; 75% cen t o f the residue todaughter
,and the balance
, $120, to a faithful servant . H ow
much did e ach rece ive ?69. A house that co st $3 125, was rented forWhat per cent. did it pay on the inve stment70 . A gro cer bought 60 gallons o f milk by be er measureat 4 cents a quart
,and so ld it by w ine measure at 5 cents a
quart. H ow much was his gain ?
120 AR ITHM ETICAL EXAMPLES.
7 1. If I borrow $1000 in Mass . and lend it in New York,
how much do I gain in 1 yr. 3 mo . 20 da. ?72 . The to tal population of America is 70415000
,3 9% of
which are Protestants ; the total population of Europe is282823 000
,2 3 % of which are Protestants . H owmany more
Protestan ts in Europe than in America ?73 . If3 00 sheep require 150 A . 3 R. 3 6 P . of pasture
,how
many acre s w il l 450 sheep require ?74 . I sent $123 00 to my agent in New York
,w i th which
to purchase flour at $10 per barre l , after deducting his commission of 2 1' H ow many barrels of flour did I re ce ive ?
75. A manufacturer effe cted an i nsurance U pon his factoryand machinery
,valued at $20000 , paying an annual premium
of in the se cond year the e stablishment was damaged byfire to the amount of $1560 . H ow much did he save by theinsurance76 . Average the follow ing account
JOHN LYMAN.
1860. 1 6
June 12 To M dse. | 530 00 HJun e0
24 By draft at 3 0 da. ,480 00
Sept. 12
I428 00
HAug. 20
'cash, 00
Oct. 28 440 00 Oct. 8 1
80
00
77 Thre e perso ns purchased a blo ck of tenements for$350000, .of which A paid $150000 ; B , $80000 ; C, $120000 ;the net proceeds of the rent were $2 1000 . H ow much shouldeach receive ?78. H ow much gold , silver and copper in an eagle, i ts
w eight be ing 10 pw ts . 18 gr.79. A capital ist invested of his money in R . R. stock ,
which depreciated the remainde r he inve sted in reale state
,which advanced \ 15% ,
and thereby he gained $1500 .
H ow much did he gain in bo th inve stments ?80. Boise
,Smith 67. Co . failed in busine ss ; the ir indebted
ne ss was $75000 ; the ir assets w e re, Cash, $3 000 ; Mdse., $15500 ; Store, $28000 ; B ills Receivable , $5500 ; the expense s of
AR ITHM ETICAL E XAMPLE S.
each,and one of $50 be came worthless ; I dispose of the re
mainder at par,and thus make $520. What was the amount
of bills purchased ?89. I bought 23 45 bushe l s of wheat at and imme
diately sold i t at on a note of 6 months,which I go t
discounted at bank at 7 per cent. H ow much did I gain ?90 . I sent $9020 to my agen t in Chicago, who purchas ed
grain at an average price of per bushel,and charged
ommission . H ow manyO
b ushels did he buy ?91 . On the first of Jan .
,1862
,there were 10869 miles of
railroad in operation in Great Britain,and the total receipts
f or the year w ere £28565355; the expenses w ere £878681le ss than the ne t receipts. H ow many dollars U . S. currencywere the ne t receipts per mile, sterl ing bills being quoted at
92 . The number of men sent into the army,up to Jan . 1
,
1863,from Illino is
,Ohio
,Pennsylvan ia
,and New York
,was
proportional respective ly to the numbe rs 3 4,40 and
44g; Ohio sen t 3 4743 mo re men than Illinois . W hat numb er of men did each State furn ish ?93 . A farmer exchanged 25bu . 3 pk . 3 qt. of corn at $ 80
per bushe l , for 3 2 yds . she e ting and 8% yds . broadclo th . A l
low ing 1 yd . of broadcloth to equal in value 24 yds. of sheeting, what was the amount paid for each ?94 . If I make a profit of 15T
5T% by se ll ing Worcester’s
D ictionarie s for $ 85 above the co st, how much must l advance on the price to realize a profit of95. A farmer so ld 4 loads of cats
,averaging 35 bu . 3 pk .
7 qt. each,for H ow much are 100 bu. 3 pk . worth
at the same rate ?96 . Thre e men engaged in the manufacture of pails ; A put
in $2550 for 8 months ; B ,a sum not specified fo r 12 months ;
C, $1080 fo r a time no t spe cified . A re ceived for his stockand pro fit $3 400 ; B , $4200 for his ; C, $1485 for his. R e
uired B’s stock and C’s time.(1
ARITHM ETICAL EXAMPLES. 123
97 . A man has twb sons,one l iving in New York
,the other
in Massachusetts ; he w ishes to place at interest $1000 foreach
,so that the amounts shall be the same in 5yr. 7 mo . ;
he supposes he has accomplished his obj ect by loaning thegiven principals
,one in New York at simple interest ; the
othe r in Massachusetts at compound interest, payable semiannually. What is the difference be twe en their re spectiveamounts98 . Bought 42 lb . of coffe e at the rate of 35lb . for
and 75 lb . more at the rate of 7 lb . for sold thewhole at the rate of 9 lb . for H ow much did I gainor lose ?99. If 7 cwt. 2 qr. 18 lb . of sugar cost how muchsugar can b e purchased for100 . For what sum must a store and contents
,valued at
$25640 , b e insured , so as , in case of its destruction, to recoverthe entire value of the building and conten ts and the premiumof 2 per cent. ?10 1. A person trave led fromNew York to Harrisburg in
12 days,walking 4 miles the first day
,6 miles the second
,8
miles the third,and so on . H ow far is Harrisburg fromNew
York102 . The to tal length of mail routes in the U. S.,
June 1,
1861,was 1403 49 mile s the total annual transportation was
54455412 mile s . Allow ing that no mails w ere carried on
Sunday,how many time s per day, on an average
,w ere the
mails carried over each route103 . A commi ssion merchant receives 125 bbls. of flour
from A,150 bbls . from B
,225bbls. from C ; he finds on ih
spection that A’s is 10% b etter '
than B ’s,and C’s is 5T5T% b e t
ter than A ’s ; he sells the whole lo t at per barrel,
and charge s 4% commission . H ow much must he remit toeach ?104 . A man sold a farm of 165 A . 2 R . 3 2 P . at
124 AR ITHM ETICAL EXAMPLE S .
per acre,and took a note payable in 5mo . 15 da .
,at 7% in
tere st ; w ishing the money fo r immediate use,he go t the no te
discounted at a bank . H ow much did he re ce ive ?105. I w ish to l ine the carpet o f a room
,6}yd . long and5-
‘T
yd . w ide , w ith duck , g yd . w ide . H ow many yds . Of' l in ing
must I purchase,if it w ill shrink 4% in length and 5% in
w idth106. Bought cloth at per yard . What must b e
my asking price , that I may fal l on i t and still mak e2 1% on my purchase ?107 . A ,
B and C engaged in partnership w i th a jo int capital of $3 000 ; A putting in stock fo r 8 months
,B for 9
months,C fo r 12 months ; A’s part o f the profits was $64,
B’s and C’s $84 . Required the capital of each .
108. What i s the ne t value in Chicago of a sum due inParis of 63 00 francs, which is se nt to Liverpool , at 1% com
mission ; exchange , francs to £1 ; a draft fo r the net
amount in Liverpool is drawn on Boston at 7% premium,after
deducting commi ssion the proce eds of this bill being re
mitted to Chicago in a check at 5% disco unt ?109.
What is the cash balance of the fo llow ing account onDec. 3 1
,at 7 per cent. ?
J AM E S H ANSON.
I
110 . In the battle of Shiloh , Apr il , 1863 , 4% of the Federalarmy engaged w ere slain upon the fie ld ; 19 were w o undedand the prisoners w e re 77 more than 50% of thewounded,also 2 355 more than the k illed . H ow many men were inthe engagement ?111 .
A merchan t bought 64 yd . broadclo th, which was 1gyd
. w ide, for $5per yard ; but the clo th be ing wet, shrunk
126 A R ITHM ETICAL EXAMPL E S .
the salary of a book-k eeper, i t was arranged that each partnershould keep a strict account of all his expenditure s and re
ce ipts , and report at the completion of the job , at which timethey Would have a general settlement. At the time of setlement they found their affairs standing as fo llows
,viz. : A
had paid out for building material and wagesand had rece ived from Gwinn Co . $12790 ; B had paidout for building material and wages and hadreceived of Gwinn and Co . $15842 . There was due the
hands and fo r material‘, What was their entireprofit ? H ow much was due from Gw inn dz Co ? How
much should be paid to A and B respective]y120 . Bought a bill of goods for $1500 , payable in 3
months, g in 6 months, and the remainder in 9 mo nths.
’
H ow
much ready cash ought I to pay for the goods, money beingworth 6 per cent .?12 1. If a ship sail 5 mi. 3 fur . rd . per hour
,how long
w i ll i t be in going 16 18 mi. 2 fur. rd. ?
122 . A house that cost $15725, rents fo r theinsurance i s A and the repairs T% % each year. What rateof interest does it pay
123 . A merchant, having sold a number of yards from apiece of cloth
,found there were yards left
,which was
65 per cent. l ess than the quanti ty cut Off. Required thenumber of yards in the piece at first.124 . The capital stock o f the Boston andWorcester Rail
road Company i s $4500000 , and i ts debt $126000 . Its grossearnings in 1861 w ere $92893 2 , and i ts expenses $5203 3 8 .
If the company pai d expenses,interest on '
its debt o f and
reserved $1853 4, what dividend would a stockholder rece ivewho owned 25 shares of $100125. If gain in 9 mo . 19 da.
,what princi
pal is required to gain in 2 yr. 5mo . 26 da .?
126. Find a number between 893 and 93 1, which shall
AR ITHM ETICAL EXAMPLES. 127
have w ith each the same greatest common diviso r that theyhave w ith each o ther .127 . A merchant has $2 16 due him,
to b e paid in 7 months ;but the debtor agrees to pay one-half ready money
,and
13o f
the remainder in 6 months. What time should he b e allow edfor paying the balance ?128 . Imported from Havre 120 baskets of champagne , 12
bottle s each,5% breakage , duty 4075, fre ight and o ther charges
and the who le cost H ow much did itcost per bottle in Havre ? how much in store ? and whatmust I charge per bottle to clear129. H ow much butter at $ 3 77} a pound, must be given
for 12 gal . 3 qt . of mo lasses,at. $75 a gallon ?
13 0 . The paid- in capital of the Uni ted States InsuranceCompany in 1863
,was $879720 ; i ts receipts for the y ear
w ere $3 14470 ; and its losses and expenses $13 8526 . Whatrate of dividend could it declare ?13 1. H ow many fee t of boards w ill i t take to inclo se a
garden 40 ft. 6 in . long,and 3 0 ft. 3 in . w ide
,w i th a clo se
fence 7 ft. 6 in . high ?13 2 . A pork merchant charged 12% commission, and
cleared after paying out for all expense sof packing ; if the pork co st him $ 065; a pound, how manypounds did he pack ?13 3 . H ow much more can a bank make in 528 days
,w i th
$10000 , by discounting notes on 45 days’ time,than by dis
counting them on 3 0 days,the rate o f discount being and
the profits in bo th cases retained in bank till the expiration of
the time ?13 4. Sold Hiram Jones goods to the amount of $2084, oncredit for 6 mo . from Sept. 20 , 1862 ; Oct. 8 he paid me
$520 ; Nov . 20, $3 40 ; Dec. 25, $800 ; J an . 12
,1863
, $100 .
When,in equity
,ought I to re ce ive the balance ?
135. When a bill on Paris fo r 28965 francs costswhat pe r cent. is the rate Of’
exchange above par ?
128 AR ITHM ETICAL EXAMPLE S .
13 6 . The average dividends o f all the savings banks in Mass .
in 186 1,w ere and $1943 53 2 was distributed among the
depositors. W hat were the aggregate deposits in the savingsbanks ?13 7 . A sell s goods which had cost $800 , to B at an ad
vance of sells them to C,and gains 111
975Ofwhat hehad paid . What per cent. would A have gained had he soldthe goods to C for the same which B rece ived13 8 . There was paid in New Orleans $7840 for £1600 draft
on L iverpool . At what per cent. premiumwas i t purchased ?13 9. If i t require $900 to support a family of 12 persons
,
41 weeks and 1 day,how much at the same rate w ill b e re
quired to support a family of 24 persons 22 weeks 65days ?140 . Subtract 2 fur. 10 rd . 5yd . 2 ft. from 2 fur. 11 rd.
1 ft. 5in .
14 1.
rThe Cleveland,Columbus and Cincinnati Railroad re
ported its earn ings for 1863 to be $2 145080 and its expenses,
$96 1785; the company invested in new depo ts,engines
,cars
and railroad stock, $55173 9 ; Aug. 1,1863
,i t de clared a 6%
dividend of its paid- in capital of $5000000, and Jan . 1,1864
,
another 5% dividend . What surplus revenue still remained142 . The stock of three partners, A ,
B and C,was $2400,
$2000, and $1800 , and the ir gain $768, $960 , and $1152 re
spectively ; C’s stock con tinued in trade 4 months longer than
B’s . H ow long was the money of each in trade ?143 . If 1275 of what is rece ived for goods i s gain, what is
the gain144 . I sold i of my goods at an advance of 2575; 7
36 of
them at a loss of 8% 21
0of them at a profit o f and of
them at a discoun t Of For what o f the co st must theremainder be so ld in order to lo se 5% on the who le145. The charter of a new railroad company limi ts the stock
to $1500000 , of which 3 installments of and
respectively,have been paid in ; the co st of construction has
13 0 AR ITHM ETICAL EXAMPLES.
the balance was a 5% dividend on the capital stock .Required
the capital stock .
$66, which was 40% le ss than the cost. What was the co st ?155. W hat is the value of 25 hhd . sugar
,each we ighing 12
cwt. 3 qr. 16 lh. ; draft, 3 lb . per cwt.,and tare 10 lb . per
cw t., at per cwt . ne t ?
156 . A man having $285, gave of i t for bushe l s ofclover seed . What was the price per pound ?157 . A merchan t imported from Bremen 40 pieces of
linen of 35yards each,on which he paid for dutie s
,at
and o ther charge s to the amount of Whatwas the invoiced value per yard ? and the cost per yard afte rdutie s and charge s were paid ?158. At the battle of Frederick sburg, Dec. 13 , 1862 , the
losses of the Federal army in killed,wounded and prisoners
,
were in the proportion of and 97 respective ly,and there
w ere 793 0 more prisoners than killed . Required the total lo ss.159 . H ow many sacks of coffe e
,each containing 108 lh.
,at
1s . 6d. per pound , New York currency, w ill pay for 135
yards Of broadcloth,at $3 § per yard ?
160 . A buyer expended equal sums of' mo ney in the purchase of wheat
,rye and oats ; in the sale s he cleared 7% on
the wheat,5% on the rye
,but lost 1575o n the oats ; the who le
amoun t re ce ived was $1782 . What sum did he expend fo reach kind of grain ?161 . I rece ived an 8% dividend on New York city ra i lroad
stock,and invested the money in the same sto ck at My
stock having increased to $13 750, what was the amoun t ofmy dividend
ARITHMETIOAL EXAMPLES . 13 1
162 . Great Britain and Ireland have an area of 112 190square miles
,and a population of 29169400 . Supposing the
familie s to average 5persons, and the whole area to b e equallydivided among them,
how much land could each family po ssess ?163 . If mo lasse s co st 20% less than $ 75 a gallon, and it
be so ld at a profit of at what price is i t sold ?164. The ” quick step in marching be ing 2 paces of 28inches each
, per second, what is the rate per hour ?165. H ow much time must a general allow fo r a detach
ment of soldiers,marching quick step
,to reach a place 50
miles distant,giving the men a halt o f 15hours ?
166 . A capitalist ho lding bo nds"
of the Columbus and
Indianapol is Railroad,to the amoun t of $27000 , exchanged
them at the marke t price of for capital sto ck of the same
company,worth the bonds drew 875annually, while the
sto ckholders received two dividends during the year ; the firsto f 3
2‘
and the second o f 475. H ow much did the capitalistgain annually by the exchange ?167 . The population of Mass. in 1850 was 994500 ; in
1860,1 13 1191 ; of Penn . in 1850
,23 11800
,and in 1860
,
290 13 09. H ow much more was the increase per cent. inPenn . than in Mass. for the ten years ?168 . If the interest of for 1 yr . 10 mo . 16 da. is
what w ill b e the amoun t ’
of $5772 from Oct. 26,1859
,to Apr. 12
,1864 ?
169. Find the day of maturity,the time to run
,and the
pro ceeds of the follow ing no te :
$575Tfifisfi
CHICAGO,March 2
,1864 .
Six months after date,I promise to pay to the o rder of
Marks Willis,five hundred seventy-five
7633—6 do llars, value
rece ived .
H IRAM BE NNET.
Discounted at a bank,Apr. 10
,at
13 2 ARITHMET ICAL EXAMPLES.
170 . If 8 men can perfo rm a piece of work in 3 2 days,
how many men must b e added to the number to perform thework in 8 days ?17 1 . The total value of al l the property
,real and personal
,
of the Free State s in 1860,was $10852081600 ; and o f the
Slave States, $52253 07000 . The products o f the Fre e States
for the same year were valued at $417805l4 l6 of the SlaveState s
, 331149567540 . H ow much greater per ,cent. of the
capital inve sted,were the products of the Free States
,than o f
Slave States ?172 . In what time w ill any sum of money amount to 10
time s i tse lf at 7 per cent.173 . A me rchan t sold a. quantity of goods for $480 , and
lose s at the rate of 9 per cen t. What ought he to have so ldthem fo r to realize a profit o f 7 per cent. ?174 . If a man dig a ce l lar 8 fe e t square and 6 fe e t deep in
2 days,how long w ill i t take him to dig a similar one 12 fe e t
square and 7 feet deep ?175. The cost in store of 40 puncheons of Jamaica rum
,84
gal . each,was duty 15% leakage and charge sWhat was the cost per gallon in Jamaica ?
176 . In the examination of a class,160 question s w ere sub
mitted to each of the five members ; A answe red 13 0 ; B,125; C, 1 15; D ,
122 ; and E,158 . What was the standing
of the class177 . If an army of 5000 men have provisions for 15days
,
at the rate of 20 oz . a day to each man ,and they b e re info rced
w ith 3 000 men,upon what daily allowance must each man b e
put that the same pro vis ion may last 20 days ?178 . The British Industrial Exhibition remained open 141
days,and the average number of daily visitors was 4283 1
the whole amoun t received for admission was £603 917 1.
W hat was the price of admission ?179. W hat per cent. of 2455is 5, of
13 4 A R ITHM ETICA L EXAMPLES .
10% he afterwards so ld the same kind o f Hour at perbarre l . What per cen t. did he gain at the latter price ?192 . H ow shall a me rchan t tailor mark coats that costso as to fall 20% from the marked price, and ye t make
25% on the coats ?193 . W hat must 2} lb . of tea be sold for
,if 225lh. cost
$14, and the retail profit is194. The area of Rhode Island is 519698 acres
,the cash
value of which in 1860 was $19488675; the area of De lawareis 1004295 acres
,o f which the cash value was $3 1426357 ; at
the same time there w ere 2290 slave s in Delaware. Now,i f
by freeing the slaves in the latter State the cash value of thefarms would become the same per acre as in Rhode Island,how much would the State gain, reckon ing the slaves at anaverage value of $250195. 3} of 28 is ft, of how many of 55?196 . A man owed $420 , due Oct. 1 , 1863 ; he payed part
of it,Aug. 15
,1863
,and the rest Jan . 1
,1864 . What were
the paymen ts ?197 . If 3 72 men in 7 ; days, of 11 hours each, dig a canal o f
7 degree s of hardness, 3 10 yards long, 55yards w ide , and 2 3,yards de ep
,in how many days, of 8 hours each , w ill 27 men
dig a canal of 4 degre e s of hardness, 270 yards long, 7 yardsw ide and 3 ; yards deep ?
198. The net proceeds of the sale of 1000 tons of hay,at
$20 per ton, after deducting $875 fo r charge s, w ere $183 25.
W hat rate of commission was charged199 . W hat principal w ill gain $2 13 , at 75per cen t. , in 2
yr. 4 mo . 12 da. ?200 . The area drained by the ponds and lake s which sup .
ply the city of Brooklyn w i th water is 6217 square mile s,upon which the average annual fall o f rain i s 3 85inche s ; theaverage dai ly supply to the city is 20000000 gallons . H ow
much water falls fo r e ve ry gallon co nveyed to the city ?
AR ITHM ETICAL EXAMPLES . 135
201 . What is the least common multiple of 943,103
and 7{6202 . An army which has been three times decimated inbattle now numbers only 14580 men . What was the original number in the army ?203 . Sold 2978 bushels of wheat at per bushe l in
vested the proceeds ih sugar, as per order, re serving my com
mission of 5% for sell ing and l %% for buying, and the expenseof shipping
,H ow much did I inve st in sugar ?
204 . A and B had the same amount of money ; A spent7675of his money for land
,and B lo st by gambl ing a sum
equal to of what both had at first,when both toge ther
had W hat sumhad each at first,and how much had
each left205. There are 20 college s in New Yo rk
,having an aggre
gate o f 118060 vo lume s in all their l ibrar ie s . What is theaverage value of the se l ibrarie s
,at $5per volume ?
206 .What per cent . of a number i s 40% of gof it ?
207 . H ow far do e s a man walk in planting a field of corn207 ft. square , the rows being 3 fee t apart and 3 fe e t fromthe fence ?208 . A merchant owes $440 , payable in 20 mon ths, and
$896, payable in 24 months ; the first he pays in 5mon ths,and the second in , o ne month after that . H ow much shouldhe pay
,allow ing 8 per cent . per annum
209. Willis, Markham,Co . ofNew Orleans import from
Liverpoo l 8 piece s of Turkey Carpe ting,35 yd . each
,at 6 4 .
per yd.,duty 3 00 yd . woo len goods at 4s . per yd.,
duty 1875, and 25 piece s of silk , 18 yds. each, at 2 s . 6d. pe r
yard,duty Required the whole amoun t of duty
,allow
ing the value o f the pound ste rling to b e2 10 . Paid dutie s at the rate of 9 per cent . on 50
cask s of raisins,tare 15 lb . per cask ; allow ing the gro ss
w e ight o f each cask to have been 1 15 lb .,W hat was the in
vo ice value pe r poi
un’
d ?
1 3 6 ARITHM E TICAL EXAMPLES .
2 11. The total value o f real e state and personal propertyin Californ ia in 1850 was $22 161872 ; in 1860, $20787461 3What was the total increase
,and increase pe r cen t.
2 12 . Divide $435 among A,B,and C
,so that f, of A’s
money shall be equal to 3 o f B ’s,or 3 of C’s .
2 13 . James Hayne s buys a bill o f merchandise in New
Yo rk,at cash price
,to the amount of and give s in
payment his note at 3 months at W hat must b e the
face of the note ?2 14 . If 6 men do as much work as 14 women
,and 10
women as much as 27 boys,and 14 boys as much as 25girls,
and 18 girls bind 250 sheave s in an hour,how many sheaves
can 24 men bind in the same time ?2 15. If A owe s $500 due in 6 months
, $400 due in 4
months,and $3 00 due in 7 mon ths
,and pays 3 of the whole
in 3 months,when ought the remainder to be paid ?
2 16 . The population of Charle ston , S. C_ m 1850 was
42982,and in 1860
,40575; the populatio n of New Haven ,
Conn .,at the same date s was 203 45, and 3 9266 , re spectively .
W hat was the increase per cen t. in New Haven , and what theloss per cen t . in Charleston , dur ing this time ?
2 17 .The interest of $4000 for 1 month and 6 days is $3 6,
what i s the rate per cent .2 18. W illiam Hatch, born Feb . 29, 1844, rece ived fromhis father a presen t o f $50 on each birthday till he became ofage .
What was the amoun t rece ived ?
2 19. If 3 of a hogshead o f o il i s w orth $48, what i s thevalue of 1
85o f the remainder
220 .Bought a quantity o f w ine for at $ 85 per
gallon ; but a part having leaked out,the remainder was sold
at 40% advance, and the original co st was real ized.What
quan tity leaked out22 1 . In 1860 there w ere 7766 manufacturing e stablish
ments in Massachus e tts , w i th an aggregate capi tal of $13 3
13 8 ARITHMETICAL EXAMPLES.
228 . Bought a number of bale s of velve t, each contain ing126 yards
,at the rate of $10 for 7 yards, and immediately
so ld the whole at the rate of $13 for 9 yards, thereby making$26. Required the number of bales ?229. If eggs are bought at the rate of 10 for $ 25, and soldat the rate of 6 for $ 16, how many dozen must be sold togain $20 ?
“7 23 0 . In what time at 12% w ill $240 amount to $720 ?23 1 . I have $58650 to invest, and can buy New York Central 6 ’
s at or New York Central 7’s at H ow
much more profitable w ill the latter investment be than theformer per year ?2 3 2 . In 1862 there were 3 8 instructors in Harvard Un iver
s ity, and the ratio of teachers to students was 1 to 22 ; o f
teachers to alumn i,1 to 189 ; of alumn i to the volumes in the
l ibrary,9 to 190 . Required the number of students
,alumn i
,
and volumes in l ibrary.
23 3 . One thousand dollars was to be divided among A,B
and C,in the ratio of 3, 3 and 3, but C rel inquished his share
how much did A and B e ach rece ive2 3 4 . A wholesale merchant sen t a quantity of goods intothe country to be sold at auction
,on a
,
commi ssion ofWhat amoun t of goods must be sold
,that his agent may buy
produce with the avails to the amount of $1910, after retaining a commission of235. H ow many yards of cloth
,13 yards w ide, are required
for a garment contain ing 23 square yards,if the clo th ln being
sponged shrinks 10% in length and 875in width?23 6. The products of Rhode Island in 1860
,were valued at
$52440000 , or $3 00 per capita ; of De laware, $16159000 , or$143 per head . What was the differen ce in population in thetwo States ?2 3 7 . If f’; of A’s money equals ‘
7of B ’
s,what part of B’
s
money equals 3 ofA ’s ?
ARITHMETICAL EXAMPLES . 13 9
23 8. What are the proce eds of a note of $5600, payable in6 months
,discounted at
2 3 9. If the annual ren t of 2 3 A . 1 R . 27 P . of land b ehow much w ill b e the rent of 71 A . 20 P. ?
240 . The Julian Calendar assumed the year,3 65da . 6 h.
,
instead of 3 65 da. 5h . 48 min . sec.,i ts true length . In
how many years was 1 day gained ?241 . I got a note of $800, payable in 4months, discounted ata bank at and put themoney rece ived
,upon interest at the
rate of 7375. W hen the no te matured,I paid it w i th the pro
ce eds of a bank-no te,at 5mo .
,discoun ted
,also at and
,as
before,paid this w ith the pro ce eds o f a third
,which matured in
one year from the date of the original note,at which time I
collected the sum due,and paid the bank note W hat did I
gain by the transaction242 . If the interest of £179 12 s . l ld. for 1 yr. 7 mos.
,is
£14 4 s . 55da what is the rate per cent .243 . Three persons found $120 , which they agreed to share
in the proportions of 5,7 and 8. H ow much did each re
ceive ?
244 . A commission merchant sold goods to the amount of$593 7 fo r which he charged a commission of gof one percent . What was his commi ssion ?245. The public debt of the Un ited States
,March 1
,1864,
was as follows : Immediate Liabilitie s, 354872 3 7286 8 ; OldPublic Debt
,31867447412 55; 73 0 Bonds, $ 1 3 87723 00 ; U .
S. No tes,
Fractional Currency,
15; Twenty Years Loans and Bonds, $51227000 ; TreasuryNotes
, Oregon W ar Debt, $10 16000 ; Cer
tificates of Inde b tedness, $13 612 1650 and 5-20 Bonds $510
the amount in the Treasury b eing $941 17what was the debt ?246 . A has $12000 loaned in Connnecticut, and $10600
loaned in New York . On which sumi s the legal interest thegreater
,and how much per, year ?
140 AR ITHMETICAL EXAMPLES .
247 . A man took out a life policy for $3 000, at the rate ofper $1000 . What summust he deposit in a savings
bank,the compound interest of which at payable semi
annually,shall discharge his annual premium?
2 48 . A merchant bought 500 barrels of flour at a.
barrel, ,
and sold it immediately at a barrel,receiving in
payment a note due three months hence,which he had dis
counted at a bank at What did he gain on the flour ?249. If a staff 2 ft. 9 in . long
,cast a shadow 1 ft. 13 ih .
,
what is the hight of a pole which casts a shadow 63 ft. ?250 . The gross earn ings of the Michigan Southern Railroad,
for the year ending March 1, 1864, w ere $3 3 080 11 the expenditures , $1669006 . It paid intere st to the amount of$690000 , and a 10% dividend upon its preferred stock of
$2893 600. H ow much remained for a sinking fund ?251 . If 3 of a ton of coal be sold for what 3 of it cost, whati s the gain per cent.252 . A’s money is to B ’s as 3 to 4 ; 3 ofA’s money placedat intere st for 3 yr. 8 mo . 15 da.
,at 6 per cent, w ill amoun t
to H ow much money has each ?253 . Sold wheat at 33 per bushel, and gained
For what should it have been sold to have lo st254 .
What i s the cost of a 90 days’ bill on Philade lphia,to
the amoun t of $1000, at 375 premium,and intere st off at
255. The interest of a certain sum for 1 mo . 19 da. at 13 3per cen t . i s $ 866. W hat i s the principal ?
256 .The Illinois Central Railroad so ld in one month 26780
acre s of l and at an average price of per acre, and an
average credit of 3 yr. 6 mo . What was the cash value o f
the sales, money be ing wor th257 .
A and B are partners ; A’s sto ck is to B ’s as 5 to 8 ;after 4 months A w ithdraws 3 of his , and B 3 of his. H ow
shall the year’s gain, $920 , b e divided ?
142 ARITHMETICAL EXAMPLES .
bacco are worth 10 .
—1; pounds of sugar, what w ill 90 pounds ofsugar cost ?267 . What must be paid in Boston for a draft on New
Yo rk at 3 0 days,for $4500 , exchange be ing at 5 premium
268 . The co st of producing fine salt at the Onondaga SaltWorks
,is 1 1} cen ts per bushel , and coarse salt 5 cents ; in
1862,1884697 bushels of coarse
,and 53 15694 bushels of fine
salt w e re produced,and sold at an average price of 19 cents
per bushel . What was the per cent. of profit ?269. At what rate must a note
,payable in one year, w ith
out grace,be discounted to produce 6% interest ?
270 . The factors of acertain number are 165, and
19 -1 what i s o f gof % of the number ?a) ?
271 . A bank has $2000O loaned on call at 5% how muchis the daily interest
,reckon ing 3 65 days in a year
272 . Bought a horse for $110 ; for how much must he besold to gain273 . The total value of real estate and personal property
in the Un ited State s in 1850 was $7 13 5780228 ; in 1862,
$16159616068. What was the actual increase ln property ?and the increase per cent. in 12 years ?274 . A man
,engaged in business w ith a capital of $25000
i s making 10 71, per cent . per annum on his capital' ; but onaccount of fail ing health
,he is obliged to quit business
,and
loan his money at 7 per cent. H ow much do es he lose in 2yr. 7 mo . 20 da.275. If one cubic foot of anthracite coal w e ighs 56 1b . ,
whatmust b e the length of a b in 8 ft. wide and 6 ft. de ep , to hold14 long tons of coal276. A and B inve sted equal sums in trade ; A lost 20%
o f his money, and B gained A’s money was then75% o f B ’s what sum did each invest ?277 . In what time w ill $4500 gain at 5per cent. ?
AR ITHMETICAL EXAMPL E S. 143
278 . A merchant bought goods in Chicago to the amountof $850 , and gave his no te , July 1, 1860, on interest after 2months ; 4 months after the no te was given
,he paid $400,
and 6 months after the firs t payment,he paid $3 60 . W hat
was there due Sept. 19,1862 ?
279. Iowa produced in one year 183 50000 bushels of
wheat,valued at $7200000 ; 60000000 bushels o fcorn, worth
$ 12 per bushe l 10000000 bushe ls of oats,valued at $1500
000 ; 3 000000 bushe ls of potatoes,worth $ 25 per bushe l .
Required the whole number of bushe ls and the ir total value.280 . If the price of a farm of 160 A. 2 3 . 20 P. be $7850.
25,what w ill b e the price of ano ther farm
,contain ing 120 A.
3 0 P . ,if 3 acre s of the latter b e worth 4 of the former ?
281 . A man bought 840 bushels of cats in New York at$ 35per bushel, and so ld them in Connecticut forThe transactions be ing made by weight
,how much advance
upon the cost was the sell ing price per bushe l282 . A gentleman
,traveling east from Lawrence
,Kansas
,
in 95°10
'
W . Long. found, on arr iving at Bo ston,that his
watch,
‘
an excellent time -ke eper,was 1 h. 3 6 min . 28 sec.
slower than the time at Boston . What is the longitude ofBo ston ?283 . The revenue of the English Government for the year
1861 was $3 3 2 142625, and the expenditure s fo r the sameyear exceeded the revenue by 3 —1
5much was the
national debt increased during the year ?
284. A and B can do a work in 1041} days ; B and C in13
31 days ’
; and A and C in 12 days. In what time wouldeach do the work alone ? and how long would it take them
,
working all toge ther, to do it ?285. The ne t proceeds of a shipmen t of hay
,sold at $14
pe r ton,after deducting a commission of and $500 for
o ther charge s,w ere $6290. H ow many tons of hay w ere
shipped ?
144 AR ITHM ETICAL EXAMPLES .
286. In how many years is a day gained by the GregorianCalendar
,which allows for the fraction of a day by adding 97
days in 400 years287 . H ow many shares of' $50 each must be bought at 25%discount
,brokerage l é
fiyé , and sold at 16% discount, brokerageto gain $13 4 ?
288 . Bonds at 25% premium,brokerage cost
more than the face ; what is the face ?289. In the United Kingdom of Great Britain 593 284200
le tters were delivered in the year 1861,of which 486679200
be longed to England and Wale s,or 24 to each inhabitant ;
50049000 belonged to Ire land,o r 9 to each inhabitant ; and
56556000 to Scotland,or 18 to each inhabitant. What was
the population of the Un ited Kingdom?290 . A facto r receives and i s directed to purchasecotton at $289 per bale ; he is to receive 4% commi ssion.
H ow many bale s does he buy ?291. B .F. Sears bought a house and lot
,Apr . 1, 1863 , for
which he agreed to pay $2500 on the l 6th of the follow ingNov .
,and $1800, Apr. 1, 1864 . If he could have got a dis
coun t of 976 for present payment, how much would he havegained by borrow ing the sum at and how much would hehave borrowed ?292 . Three men engaged in the lumber trade ; A furn ished
$4000 , and B $6000 ; they gained $1680 , of which C’s sharewas $840 . Required C’s stock and A’s and B ’s gain .
293 . If a cistern 19 !Fft. long, 1021 ft. w ide, and 12 ft. deep,hold 546 barre ls
,how many barrels will a cistern contain
that is 18 ft. long,9 ft. w ide and 15 ft. de ep ?
294 . A speculator gained 25% on gof his inve stment, andlost 5% on the remainder ; his ne t profits w ere $1140 . Hadhe gained 25% on g, and lost 5% on the remainder
,what would
have been his ne t profits ?295. A lady bought 23 yards of sheeting and 575yards of
146 ARITHMETICAL EXAMPLES.
average number o f men attache d to each battery was 255ofthe average number in each regimen t ; there w ere 12 3 prisoner s unclassified . Required the numbe r of infantry and ar
tillery and the to tal surrender.3 06 . Gave o f note s at discount for $500 gold.
What rate o f premium was the go ld ?3 07 . A and B made a join t stock of $1666 , and gained
$204 , of which B had $60 more than A . H ow much did eachcontribute to the stock3 08 . A gro ce r bought 1 1 bushel s of che stnuts at abushel
,and re tailed them at 3 cents a half pint. What
profit was his gain ?3 09. July 1
,1859
,four balloon ists left St. Louis at 4 h . 3 0
min . P . M .,and landed in Jefferson Cc .
,N. Y .
,1 150 mile s
from St. Louis,at 20 minute s past noon of July 2nd. W hat
was the average velocity per minute ?3 10. If the use of for 7 yr. 6 mo . i s worth
what sum is that whose use for 10 yr. 10 mo . 20 d .
is worth3 1 1 . Forty per cen t . of brandy is alcohol . H ow muchalcoho l doe s a man drink in 52 years
,if he take 2 of a gill
of brandy 3 time s a day3 12 . A
,
house that rents for cost $8700. W hatdoe s i t pay on the inve stmen t ?3 13 . When shall a note be made payable to balance thefo llow ing account
J AM E S TYLE R .
1860. 1860.
June 12 To M dse . on 3 mo . 53 0 84 Sept. 14 By Cash,20 6 6 6 6 6 6 $ 6 2 136 '48
66 25 u u
66
~
3 0 6 6 66 6 6 6 673 9 56 Oct 3 6 6 6 6
J UIYI 5 66 6 6 6 6 6 6 (273‘
4 41 66 17 6 6 66
6.‘
16 6 6 6 6 66 6 6 194 78 NOV . 16 6 6 6 6
u 20 u u u u. 53 6 42 94 u u
3 14 . M,N
,and S
,are partners . On closing busine ss
,
they have the follow ing resources and liabil ities ; cash on
ARITHMETICAL EXAMPLES . 147
hand, $543 0 ; shop and fixture s valued at $2560 ; bills
rece ivable, $956 Barns 65 Co . ow e them $865; ten share s
in Canal R . R . stock, $1000 . They owe on no te s unre
de emed, $1865. M inve sted $2400 ; N, $3 000 , and S, $2700 .
What is the ne t gain3 15. What per cent . of an acre is 2 R. 20 P .
3 16 . In the battle of Perryville , Ky.
,Oct. 8
,1862
,the
Rebe l lo ss in killed and prisoners toge ther was 50% of thelo ss in wounded
,and the prisoners w ere T
23
of the killedVVhat per cent . of the lo ss w ere pri soners ? The prisonersnumbered 200 . What was ”
the who le Rebe l loss3 17 . The Federal loss in the same battle was 3 50 morethan the rebe l lo ss the pr isoners w ere 16% o f the en tire lo ss ;and the killed 50 more than 20% of the entire Federal loss ;the remainder be ing w ounded
,what was the ir number
3 18 . At per cwt.
,how much sugar can b e bought
for
3 19. If i t require 2250 bricks,8 in . long by 4 in . w ide
,to
pave a court 25 ft . by 20 ft., how many tiles, 10 in . long by5 in . w ide
,w ill be required to pave a walk 3 00 ft. by 8 ft. ?
3 20 . My salary is $800 a year. If I pay 25% for board,10% of the remainder for rent
,20% of the residue for clothe s,
$3 2 for books, and loan 5the remainder, what 75 ofmy salaryis un expended ?
3 21 . Inve sted $3 43 2 in Government bonds at paying1 -
41% broke rage , and afterward sold the sto ck at 12% premium
,brokerage What was my gain ?
3 22 . A merchant bought a quantity of flour at perbarre l on a credit of 3 months
,and kept it 6 months ; then
sold i t on 3 months’ credit,and gained Money be ing
wo rth for how much did he sell the flour per barrel3 23 . 1 qt. pt. i s what per cents of 2 gal . 3 } qt . ?3 24 . I own $12500 in a Mutual Insurance Company. H ow
148 ARITHMETICAL EXAMPLES .
many shares shall I possess afte r a dividend of 8% has beendeclared
,payable in stock ?
3 25. Twelve mill ion gallons of petro leum were sent toEurope from the Un ited State s in 1862 fo r $3 600000 ; the
co st of production being $ 20 a gallon , what was the rate of
profit ?3 26. What is the value of 40 casks of sugar, each w e igh
ing 12 cw t. 3 qr. 5lb .,draft tare 10;’é, at per cwt .
n e t ?
3 27 . At what rate of discount must the Illino is State 655bonds b e purchased that the person inve sting may receive 6555upon his money3 28 . Jo nes
,B rown
,Hall 65 Smith are partners ; J ones
take s 73, of the gains o r lo sse s ; B rown 21,Hall g, and Smith
the remainder. At the clo se of the year the resource s of thefirm are : Cash $6875, M erchandise $8965, Bonds and Mo rtgages $7650 , Bank Stock $3 000 ; Jones has drawn from thebusine ss $600 , Brown $350 , and Hall $190 ; the l iabilitie sare : Notes outstanding $3 640 ; Balance in favor o fReed 67. Cc .
,
$750 ; Balance in favor of Suffo lk, $2645; Jones inve sted
$63 65, Brown $5270 , Hall $4 180 , and Smith $23 20 . Whatis each partner’s in terest in the busine ss at the close of theyear3 29. W hat w ill be the duty at on a case of j ewe lry
and watches amoun ting to $2780 ?
3 3 0 . A merchant bought 16 barre ls of salt at $1}i perbarrel , and put it in to sacks o f 10 and 25lb ., each an equalnumber, sel l ing them for $ 08 and $ 20 each. What was
his profit3 3 1 . In the series of battle s from Aug. 27 to Sept . 1, 1862 ,
lbughtbefore Washington , the kill ed of the Un ion army w ere
50% of the prisoners , and the prisoners 3 3 ,l,% o f the wounded .
W hat per cent. of the wounded, and what per cent. of thewhole loss were the killed ?
150 AR ITHM ETICAL EXAMPLES .
gal. a minute, w ill fill a ciste rn 6 time s as large in 6 hours48 minute s3 43 . The earn ings of the Hudson River R . R . for Feb .
1864 w ere $472240 , which was an increase of 1 15% ove r theearnings for the same month in 1863 . H ow much was theincrease3 44 . A town
,6 mile s square
,i s div ided into 3 25 equal
farms . What mus t A . G. Dickey pay fo r one of the se farmsat per acre ?3 45. If $1500 in 7 mo . 20 da . produce what prin ~
cipal must b e loaned to gain $58 in 10 mo . 26 da.
3 46 . M and N enter into a partnership for 2 years ; Mputs in $8000, and N $2500 ; N is to do the business, andhis services are regarded as worth the use of $5500 after 6months M increase s his stock to $12000 ; at the end of 2years the partnership i s clo sed , and there i s a net gain of
$4750 . Required each partner’s share of the gain .
3 47 . A merchant bought 500 barrel s of flour at abarre l
,payable in 3 mon ths ; after keeping i t 3 0 days, he
sold i t for a barrel,re ceiving a no te payable in 3
months ; the purchase money becoming due,he got the no te
discounted at a bank to mee t it. H ow much did he gain bythe transaction3 48. What was the cost of 12 Ohio State Bonds of $500each at 1274? premi um, 3% brokerage ?
3 49. At the battle of Pea Ridge,March 7
,1862
, T4
;of the
who le loss of the Rebel army were prisoners the killed were500 less than the prisoners
,and the wounded were 3 00 more
than twice the killed . What was the to tal Rebel loss ?
350 . If a man, by traveling 9 hours each day, can go 23 4miles in 15days
,
how far can he travel in 3 0 days o f 8 hourse ach351 . H ow many shares of min ing stock at 8055must be
ARITHMETICAL EXAMPLES. 151
sold in order that the proceeds inve ste d in Californ ia 8 ’
s at108% may yield a profit of $9603 52 . The duty on 1000 drums of figs
,each contain ing 14
lb .,invo iced at 6 cents per pound , was What was
the rate of duty ?3 53 . H ow much was the New England currency depre
ciated at the adoption of Un ited State s money,when £ 1 was
worth $433 54. H ow much had New York currency depreciated at
the same time3 55. H ow much had New ,York currency depreciatedbelow New England ?3 56 . Sold goods to a certain amoun t on a commission of
595, and having remitted the net pro ceeds to the owner,re
ce ived for prompt payment g% which amoun ted to'
W hat was the amount o f commission ?357 . What is the difference in co st be tween a draft o n
Bo ston of at l %% premium,and one on Chicago
,
for the same amount,at $56 discount ?
3 58 . A man , engaging in trade w ith $9600, found at theend of 3 years that he had gained more than 3, of hiscapital . What was his average annual gain ?3 59. In 183 7
,the silver dollar contained 412 -l grains of
standard silver,but in 1853 the w e ight was changed to 3 84
grains. The finene ss remain ing the same,one do llar of the
old coinage was worth how much o f the new ?
3 60 . A man has a pie ce of land 95} rods long and 58 ‘
rods w ide,which he w ishes to lay out in the large st possible
square lots of equal size . H ow many lo ts w ill there b e ?3 61. A ow es $1500 , of which $400 i s to be paid in 4
months, $500 in 5months, and $600 in 6 months. If he pays
the who le at once , at what time must he make the paymen t ?
3 62 .What is the duty at 2575 on 27 tons 8 cw t. 3 qr. 20
lb. of iron , invoiced at $48 per ton ?
152 A R ITHM ETICAL EXAMPLES.
3 63 . S. F. Root has cloth at per yard, and S. Smi thhas hay at per ton . If in trading Ro ot puts his clothat what should Smith charge for his hay ?3 64 . The Erie Railroad earned from all source s
,during
the year 1863, $10469480 , and the expense s of operating the
road w ere 6 1% of the earn ings. It paid for interest, rent o fother roads
,taxes and sinking fund
, $19863 15. July 1,1863
,
i t paid a 4 dividend upon i ts paid-in capital of $14000000 ,and a 5% dividend upon the same , Jan . 1
,1864 . There was a
surplus of Jan . 1,1863 . W hat was the balance
to the credit of the ro ad,Jan . 1
,1864 ?
3 65. The cargo of a ship is w orth $96000, and f; of .1 o fT7;
of the cargo is worth fl" of g of 9, of the value of the ship .
W hat i s the value of the ship ?3 66 . A Boston merchant
,having rece ived an importation
of w ine from L isbon,invo iced at 3 008 milrce s
,470 re is
,al
low s his correspondent in Lisbon to draw on him for thenecessary sum
,exchange on the Un ited States be i ng in Lis
b on 940 re is : $l . H ow much would the merchant havesaved by remitting a draft on L isbon purchased at permilre e
3 67 . H ow many eagles,each contain ing 9 pw t. gr. of
pure gold can I ge t for oz . pure gold at the mint,
allowing for coin ing expense s ?3 68. A owes B $500, payable in 4 months ; at the close of
2 months he w ishes to make such a payment as w ill extendthe time of the balance to one year. What must be the payment3 69. Massachusetts paid $2750 internal revenue tax , in
1863 , on go ld plate, at the rate of $ 50 per ounce Troy .
What was the value of the go ld plate , allow ing it to average18 carats fine
,an ounce o f pure go ld be ing w orth 2
3 70 . A,M and S form a partnership
,w i th capitals of
$5000, $10000 and $15000, respectively A draws out $500
154 A R ITHM ETICAL EXAMPLES.
U p to 1862 , was $62292500 ; the amount of toll s coll ectedfrom the se
,in 1861
,was $3 908785. H ow much ' less were
the tolls than the legal in tere st upon the sum invested inbuilding the canals ?3 80 . g, of a quarte r i s what per cent. of gof a cwt. ?3 81. The sale s of a clo thing house amount to $100000 ayear ; o f the sale s are made at a profit o f 7
2
96at a profit
o f and the remainder at a lo ss of Required thecost o f the goods .3 82 . A company of 50 men drank w ine at 2S. 6d. per bot
tle,to the amount of £10 . H ow manymen at the same rate
w ill £18 worth of w ine supply, when w ine i s wo rth 25. 3 d. per
bo ttle3 83 . What must be paid in Philade lphia for a draft on St.
Louis,drawn at 90 days
,fo r $5000 , at a premium of 1275?
3 84 . A merchant in Cincinnati w ishes to remi tto New Yo rk . Exchange on New Yo rk is premium
,but
on St. Louis premium,from St. Louis to New Orleans
$75 discount, and from New Orleans to New Yo rk 1% discount . What w ill b e the value in New York by each me thod
,
and how much be tter is the circular ?3 85. The gro ss earn ings of the Erie Railroad for 1861
w ere $5590916, and the expen se s were the
gross earn ings of the same road for 1863 were $10469480 ,and the expense s H ow much greater werethe ne t e arn ings of the gro ss earn ings in 1863 than in 18613 86 . What is 2075of 3 0% o f 50% o f
3 87 . A man can se ll his farmfor $4000 cash, o r fo r $5000 ,payable in 2 years . If he accept the last offer
,and rece ive
in ste ad its pre sen t w o rth,at 10% discount, how much mo re
would he rece ive than by the fo rmer3 88 . If he accept the firs t off er
,and loan the $4000 at 10 %
inte re st,how much le ss w o uld he rece ive at the end o f 2 years
than by the second offe r ?
AR ITHM ETICAL EXAMPLES. 155
3 89. What is the inte re st of fromNov. 27 , 1859,
to July 3,1862
,at 7 .
—j % ?
3 90 . When are paid for 8 gal . 1 pt. of milk , whatis the price per quart ?3 91. The manufacturers of Massachuse tts paid in one year
$3 2513 25 internal revenue, which was per cen t . of thesum paid by all the manufacturers in the Un ited State s. R e
quired the entire revenue from this source .
3 92 .‘If I gain on worth of sugar
,how
many do llars’ worth must I se ll to gain3 93 . A man obtained an insurance for l ife at the age of 3 7 ,
and died when 51 years old. The po l icy required annualpayments during life , at per $100 , and se cured to thehe irs mo re than the amoun t of all the premiumspaid . What was the face of the policy ?3 94 ' $3 250 ° HARTFORD
,March 6
,1859.
On demand we promise to pay Brown Gro ss,o r o rde r
,
thre e thousand two hundred and fifty do llars,for vahl e re
ce ived.
CHURCH 65 BROTH E R S.
Indorsed as fo llows : July Nov . 7,
1859, 3350 ; Jan 1 , 1860, $285 ; Aug. 10
,1860
,
July 1,186 1
, $125; Nov . 4 , 1862 , Apr . 22 , 1863 ,
July 1,1863
, $600 . What was due Apr. 1,1864 ?
3 95. A grocer bought 760 lb . of Java coffe e, at 26 centsper pound . Allow ing 16% fo r shrink age in roasting and
grinding,at what pr ice pe r pound must he se ll i t to gain
3 96 . If it require bricks to build a house who sewalls are 1 ft . 6 in . thick , 20 ft. high, and 108 ft . long
,how
many w ill build one who se walls are 2 ft. thick , 3 0 ft. high,and 3 24 ft . long ?
3 97 . A man 3 3 years old,tak e s out a pol icy f or $2000 , the
payments to cease at 50,the annuadpremium be ing per
156 AR ITHMETICAL EXAMPLES.
$100 . If he survive that age,how much more money w ill he
rece ive from the company than he pays them?3 98 . In the year 1860
,66 of all the printing in the New
England States was done in Massachuse tts ; l4§% in Connecticut ; in Maine ; 2 158% in Vermon t ;
' Rhode Island performed as much as New Hampshire ; the cost of the printing done in Rhode Island was $1073 60 more than the cost ofwhat was done in Vermont. Required the value of all theprinting done in the New England States for the year 1860 .
3 99. Paid in New York for a 3 0 days’ draft onBoston
,exchange being at 50 premium. Required the face
of the draft.400 . Smi th Boise traded in company w i th a joint stockof $8400 . Smith’s money was invested 14 months
,and Boise
10 months. The profits being equally divided,how much of
the capital did each furn ish40 1 . A man w ith the proceeds of a note for on
60 days,discoun ted at 673, purchased flour at per bar
rel,allow ing commi ssion to a factor for buying it. At the
end of 1 month he sold the flour on 90 days’ credit forper barre l ; when his note at the bank matured , he had thenote received for the flour discoun ted
,and paid his own note.
H ow much did he gain by the transaction ?402 . If 4 gal . 1 qt. 1 pt. of oil is bought for $12 25, what isthe price per gallon ?403 . The total sales of W heele r dz VVilson ’
s sew ing machine s for seven years ending Jan . 1
,1860
,w ere 3 8991 ; of
Grover Baker’s,24818 of Singer’s
,23 3 53
,and of all others
such a number that the aggregate sale s o f all kinds w ere
103 3 72 . What was the value of the miscellaneous class at anaverage pr ice of $3 0 a machine ?404 . A farmer had a dairy of 48 cows
,each furn ishing 18
qt . of milk a day, fromwhich he made 40 chee ses of 60 lb .
each in 3 0 days. He made a contract to de l iver 100 che e se sof 96 pounds each in 80 days . H ow many cow s must he
158 AR ITHM ETICAL EXAMPLES .
4 11 . H ow many bushels of corn in Illino is are equal to3 000 bushe l s in New York ?4 12 . What is the value of a house and lo t that pays aprofit of 9 per cent. by renting it at $50 per month ?413 . A draft was purchased in New York on Chicago for
$3 000, drawn at 60 days, for $2850 . What was the courseo f exchange ?4 14 . H ow many bushel s of cats in Connecticut are equalto 5000 bushel s in Iowa ?415. A farmer sold three hogs
,one w e ighing 275 pounds,
at 5 cents per pound ; a second , we ighing 3 10 pounds, at 5;cents per pound ; and the third, w e ighing 3 45 pounds
,fo r
$25. W hat was the average price per pound for the who le ?4 16 . At what rate
,of premium is Prussian coin
,when
in Un i ted States silver coinage of 183 7,is paid for
500 thalers ?4 17 . A father left his four sons
,who se age s are 15
,11
,7
and 6 years, $57770 , to be so divided that the respective
parts placed at simple interest in Conne cticut shall amount toequal sums when they become 2 1 years of age . “That arethe se parts4 18 . It is estimated that a sew ing machine do e s the work
o f six persons,and that i ts use in mak ing boots and sho e s in
Massachusetts annually save s $7500000 ; allow ing 3 00 w o rking days in a year, and 4 the average daily wage sof sho emakers
,how many persons engaged in this trade do e s
the use of sew ing machine s l eave fre e to fo llow o ther purspits ?
419 . A gro cer so l d 12 hams,each w e ighing 15 lh.
,at 21
cents pe r pound , and took in paymen t 1 load o f apple s,con ~
sisting of 18 bags,e ach contain ing 2 3 bushe ls. Required the
price of the apple s pe r bushel .420 . A merchan t in New York w ishe s to pay £3 000 in
London . Exchange on London i s premium ; on Par is,
5 francs 25 cen time s per $1 , and on Ams te rdam 40 cents to
AR ITHMETICAL EXAMPLES . 159
a guilder. The exchange be tween France and E ngland at thesame time is 25 francs to £1
,and that of Amsterdam on
England 12 ; gui lders to £1. Which is the mo st advan tage ous, the dire ct exchange
,or through Paris
,or through
Amsterdam ?42 1 . Rece ived from Charle ston 500 bale s of co tton
,each
w e ighing 560 lh.,invo iced at 9d. pe r lb . Georgia currency ;
so ld it at an advance of commission and remittedthe net proce eds by draft. What was the face of the draft,exchange be ing 1 1 discount ?422 . There were 153 3 66425 bushe ls o f bituminous coal
,
and 94 163 3 3 tons o f an thracite coal mined in the U. S. in
1860,and 25 bushe l s of the bituminous made one ton ; the
average cost of the coal at the mine s be ing per ton , whatwas the to tal value of all the coal mined ? The value in 1850be ing $7 173 750, what was the rate of incre ase in ten years ?423 . A merchant in Syracuse
,N. Y .
,purchased a draft on
Chicago for $2660, drawn at 60 days, paying1Vhat was the course of exchange ?424 . A horse which was bought for 20% le ss than his realvalue
,became injured
,and was so ld fo r 40% le ss than his
co st,at a price $13 0 below his o riginal value. For how much
was he so ld425. A gentleman sent a silver cake baske t
,w e ighing 3
pounds 9 ounce s,to a j ew e le r
,and o rde red him to take
of i t for his wo rk,and manufacture the remainde r in to smal l
de sse rt spo ons,each w e ighing 1 o z . 9 pw t . H ow many dozen
spoons ought he to rece ive426 . Two men in Hartford , Conn .
,hire a carriage for $20
to go to Waterbury, 40 mile s distan t , and back again , w iththe privilege o f taking in 3 mo re persons . Having gone10 mile s
,they take in A ; at ‘
vVate rb nry they take in B ;and
,on the ir re turn
,when 20 mile s from Hartford
,they
take in C. How much . re spective ly, shall A,B
,and C
pay
CHAPTE R VI.
1. THE W inchester bushe l is of cylindrical form,
in .
in diame ter,and 8 in . de ep . What must be the dimensions
of a cub ical box which shall contain 27 bushels ?2 . A gentleman depo sited in a savings bank for his son
,15
years of age , a sum of money,which
,at 57; compound inter
est,payable semi-annually
,amounted to $10000 at his major
i ty . What was the sum deposited3 . A grocer mixed 5 lbs. of sugar
,at 83 cts. per pound,
w ith 80 lbs., at cts. per pound,and 60 lb s. at such a price
that the mixture was worth 943 cts. per po und . Required
the price per pound of the last kind of sugar.4 . H owmuch less w ill i t co st to fence 3 2 A. 64 P . in the formof a circle
,than in the form of a square ? and how much le ss
in a square form than in the form of a rectangle,whose length
is 4 time s its w idth,the price in each case being per
rod
5. One -third of a quantity o f goods was so ld to gain acertain one -fourth to gain 15time s as much and the
remainder to gain 25time s as much What is the gainon each part
,the gain upon the who le be ing 2 1
- 6 . If a cask, 45 inche s long and 3 6 inche s bung diameter,contain 167 gallons o f w ine
,what must b e the length and
hung diame ter of a cask of the same shape , contain ing 3 14gallons ?7 . If $600 gain $72 in 1 yr. 6 mo .
,in what time “Ll $850
gain $189.83 ]g
162 AR ITHM ETICAL EXAMPLES .
16 . I owe a man the fo llow ing notes : one of $500, dueApril 1 ; one of $750 , due July 15; and one of $1750 , dueSept. 10 . The holder w ishe s to e xchange them for two note sof $1500 each, and wants one to fall due May 10 ; whenshould the other b e made payable17 . A and B traded together ; A put in $400 for 512 days,
and received 3; of the gain ; the number of do llars which Bput in was equal to the number of days it was employed intrade. What was B ’s capital ?18 . The longitude of Springfield
,Mass
,i s 72 ° 35'
45 W .,
and ofConstantinople,28
°
49' E . When i t i s 9 o ’clock A .M.
at the latter place,what time is it at the former
19. A note was given for $500, w ith interest payable ahnually, at Nothing having been paid for 10 years
,how
much did the total amount of interest due exceed the simplein terest o f the principal20 . A rectangular piece of land
,contain ing 8 A . 1 R. 3 2
sq. rd. i s5as w ide asfi
it i s long. W hat is the distance aroundit ?2 1. Bought a quantity of goods for $2500 cash , and sold
them for $3 125 o n 3 months’ credit. What did I gain,money
be ing worth22 . What is the difference between the interest and discount of $73 0 , for 5yr . 9 mo . ,
at 8 per cent . ?23 . Wishing to ascertain the height of a tower
,I erected
near it a stick fe e t high ; by measurement I found the
shadow of the tower to b e 3 65; ft., and of the stick 9 in .
at the same time. Required the height of the tower.24 . A man agre ed to work for a blacksmith for per
day and his board ; for each day lost he was to allow $ 40 .
A t the end of 11 we eks he received H ow manydays did he lose25. What is the daily interest on $63 3 00 in U. S. demand
notes,bearing 7
,35y3 interest ?
AR ITHM ETICAL EXAMPL E S . 163
26 . A ship sailed due south and due east on alternate days,
at the same rate e ach day ; at the end of six days it was foundto b e mile s south-east from the place of starting.
What was the daily rate of sail ing ?27 If a body put in mo tion move 5of an inch the firstse cond
, 5an inch the second, 1 inch the third , and so continueto increase its velocity in geome trical . ratio
,how far would it
move in gof a minute ?28. An importer sold clo th to a wholesale dealer at 10%advance ; the whole sale dealer so ld it to a clo thier atadvance ; the clo thier sold it at a farther advance of and
rece ived $1452 . H ow much did i t cost the importer ?29. The Federal debt
,Feb . 16
,1864
,was officially stated
to b e tu seeooooo. W hat per cent . is that (if the who letaxable property of the loyal States
,the latter being esti
mated at $14000000000 ?3 0 . What is the balance of the following account
,andwhen
i s i t due ?THOMAS LARDNE R .
1860. 1860 .
March 1 lTo Sundries, l43 6 l00 llMarch 25lB y D raft at 60 da.l400 l00
April 12 M dse . 548 l00 April 6 I u 3 0 u 650 00
July 16 e 3 12 00 Jun e 20 Cash, 200l00
Sept. 14 | l53 6 l00 ll Aug. 3 I84 l00
3 1 . When shall a draft for the settlement of the follow ingaccount be made payable ?
DAVID SANFORD .
3 2 . Three contractors engaged to build a piece of road for$8775; A employed 20 hands 24 days, 10 hours a day ; B ,25hands 20 days, 12 hour s a day and C
,3 0 hands 25 days
,
9 ho urs a day. H ow much shoul each contractor receive ?
164 AR ITHMETICA L EXAMPLES .
3 3 . A quantity of wheat was heaped up in a corner of asquare room forming a portion of a cone
,of which the pe r
pendicular height was 4 ft. 3 in . and the slant he ight 7 ft. 1 in .
What was its value at $16 65; a bushel ?3 4. OLIVE R W AINW R IGHT.
If the above account were settled April 6,1858
,by draft
on time, how many days’ credit should be given ?35' $1200 ‘
CHICAGO,Jan . 1
,1858 .
For value received,I promi se to pay Stephen Hopkins
,or
order,twelve hundred dollars
,on demand
,w ith interest at 7THOMAS ROBBINS.
Indorsed as follows : Jan . 1,1859
, $3 00 ; March 16, 1860 ,$350 ; Jan . 1
,1862
, $250 . W hat was due February 20,
1864
3 6. A church is 80 ft. l ong and 50 ft. w ide, and the elevation of the roof is 14 ft. ; the rafters extend2 ft. beyond theplates
,and the boarding proj ects 2 ft. at each end. H ow
many fee t of boards w ill be required to cover the roof, allowing 7
} for waste ?3 7 . D ivide $3 of a piece of cloth, which contains 453 yd.
,
into equal parts,each of which shall contain 3
52of the whole
piece . H ow many yards in each part ?3 8. If i t cost to inclose a circular field contain ing
2 A . 28 P how much w ill it cost to inclose another con
tain ing 26 A . 23 P . ?
3 9. A merchan t in New York gave $1000 for a bill onLondon of £200 . What was the rate of exchange ?40 . A gro cer desire s to mix teas worth and
w ith 140 pounds worth $ 75, that the mixture may be worthW hat quantities of each must he take ?
166 AR ITHM ETICAL EXAMPLES .
consols,bearing 3 55 in tere st for 20 years . What was the
pre sen t w o rth51. An impo rter so ld a quantity o f go ods to a who le sale
merchan t at an advance o f 10 the latte r sold them to a retailer
,gain ing and the re tail merchan t so ld them fo r
gain ing . thereby H ow much did the goodsco st the importer ?52 . There are thre e houses so si tuated that the lines con
necting them fo rm an equilateral triangle,the Side s o f which
are 70 rods in length. H ow many acre s are included in the
triangle53 . A merchant fail ing in business can pay 76 cents on ado llar . H e offers to pay his who le indebtedne ss w ithoutinte rest in five years if his credito rs w ill al low him to go on
w ith his busine ss ; his offer be ing accepted,how much w i ll his
credito rs lose in the five years,money being wo rth 7%
54 . In how many diffe re nt position s may a family of 7
persons seat themse l ve s at a table ?55. A triangular orchard has 1 tree in the first row
,3
‘
in
the second,5 in the third
,and so on in ari thme tical progre s
sion . H ow many tre e s in the o rchard,there be ing 50 row s ?
56 . What are the in terior dimensions of a cubical box thatcon tains 40 bushe ls o f grain57. H ow many stroke s of a common clock are struck in 24hours ?58 . A man w ishe s to enclose a circular fie ld which shal lcontain 34 as many acre s as it w ill require rails to build a
fence around it. The rail s be ing 15 fee t long, and the fe nce 6rails high
,how many acre s must there be in the fie ld
59 . J . Bagg 65 Co becoming inso lvent, the ir indebtednesswas $1 1666 § their asse ts w e re What o f the irindeb tedne ss can they pay, allow ing to the assigne e s 3 65o n
the amount d istributed to the creditors ?60 . The Treasurer of the State of Pe nnsylvania, N(W . 3 0
,
AR 1THM ETICAL EXAMPLES. 167
1863,made the following report of the finance s of th e State
Balance in treasury,Nov. 3 0
,186 1
,rece ipts
from ordinary sources,to Nov. 3 0
,1862
, $4047 fromextraordinary source s
,payme nts to the same
date,
Required the bala nce in treasury,Nov.
61. Rece ipts for the year ending Nov. 3 0,1863
, $4289
payments to the same date, H ow
much less in the treasury,NOV. 3 0
,1863
,than Nov. 3 0
,
1862 ?
62 . I w ish to pay a bill in Naples of 1500 ducats ; thedirect exchange is ducat ; the exchange on Londoni s of London on Paris is £1 2 26 francs ; of Pari s on
Naples is 45francs z l ducat . What is the difference betwe enthe direct and circuitous exchange ?63 . A square pyramid of cannon-balls has 12 on each sideat the base . H ow many balls in the pyramid ?64 H ow many pounds of sugar at 8
,13
,and 14 cts. per
pound,may b e mixed w ith 3 pounds at 95cts .
,2 pounds at
85cts ., and 4 pounds at 14 cts . a pound, so as to gain 1623 byse lling the mixture at 145cts. per pound ?65. What is the difference be tw een the true and bank discount of $3 000, payable in 120 days at66 . Two churche s stand on opposite side s of a street 120fee t w ide ; the he ight of the towers i s 70 and 95 fe e t
,re
spectively. Wh at is the distance from the top of one towerto the top of the o ther ? and what is the distance from the
top of each to the base of the Opposite church ?67 What is the hour when 3 of the time past noon i s 5of
the time till midn ight ?68 . E
,F
,and G start from the same po int and in the same
d ire ction to walk around a trotting course 1 mile in circumfe rence ; E take s 60 steps, of 26 inche s each, a minute ; F,
90
steps,each 28 inche s in length ; and G,
120 steps,each 3 2
inche s in length. What distance mtust each trave l, and how
168 AR ITHM ETICAL EXAMPLES.
long, before they w ill be toge ther again at the po int of starting ?
C9. A man w ishe s to tether his horse to a stake,so that i t
may graze on 5of an acre . W hat must be the length ofrope ?70. A bought a house of B
,and gave him his bond for
$6000 , dated April 1, 1860, payable in 5Equal annual installments of $1200, the first to be paid April 1
,1861 ; A took
up his bond April 1, 1863 , semi-annual discount at the rate of775per annum on the payments due after April 1
,1863
,
being deducted. What sum canceled the bond ?7 1. What i s the compound interest of $1 for 143 years,allow ing i t to double once in 1 1 yr. 11 mo ?72 . A servan t be ing ordered to purchase 40 an imals for
$40 , brought home calves at $4, lambs at and kids at$ 50 each . H ow many of each kind did he purchase ?73 . If I borrow $1000 , and agree to pay 6% at the end of
each year for the use of it,and at the end of 18 months it is
called for how much do I strictly owe ?
74 . If a cannon-ball,8 in . in diameter, weigh 128 pounds ,
what i s the diame ter of a ball weighing 250 pounds ?75. I have sugars worth 12
,14
,16
,and 18 cents a pound.
H ow many pounds of each kind may I mix to make a barrelof 260 pounds
,which I can sell at $ 165per pound, and gain
76 . A and B gain in business $5040, ofwhich A i s to have10% more than B . Required the share of each ?77 . What length of fence w ill inclose a circular field con
tain ing 10 acre s ?78. An ox, whose girth is 8 ft ., w eighs 1500 lb ; what is
the girth o f another ox that weighs 63 2 lb . 13 oz.79. X and Y entering into partnership, X at first put in
$1600 , and after 1 year added $400 to his capital ; Y put in$2000, and after 6 months w ithdrew $800 ; at the end of 2
170 AR ITHM ETICA L E XAMPLE S.
87 . A merchant mixes 13 pounds of tea w ith 7 pounds o fan infe rior qual ity
,and gains 20% by selling the mixture at
per pound . Allow ing one kind o f tea to b e w orth 20cents a pound more than the other
,what is the cost of each
per pound
88. H ow much le ss w ill the fencing of 20 acre s co st in thesquare form than in the fo rm o f a rectangle
,who se breadth is
215 the length , the price be ing per rod ?
89. A . Smith,3 4 years old
,insure s his l ife for $5000, at
the rate of per $100 ; he dies at the age of 53 . A i
low ing 6% compound intere st on all premiums paid,how
much has his policy actually co st ?
90. H ow much bank stock,at premium
,can be pur
chased for $6240 , brokerage91. A merchan t bought 200 bbl . of flour for $1665, paying
$9 per barrel for first quality, $8 fo r second , and for
third. H ow many barrel s of each quality did he buy .
92 . A cistern 15 feet deep w ill hold gallons.What i s its diameter ?93 . A young man inheri ted an estate of $40000 ; afterspending 4
)of i t
,he invested the remainder in an unsucce ssful
business,losing 3 3 g% of the investment ; w ith his remain ing
money he purchased 520 Un i ted States bonds at par, bearing6% intere st, payable in gold. H ow much was his yearly income in currency
,gold be ing 175%
94 . A Chicago merchant shipped 1000 barrels of flour tohis agen t in New Orleans, directing him to sell it, and investthe proceeds in cotton ; his agent sold the flour at $14 perbbl .
,paid $275 charge s, and bought cotton at $ 65per pound ,
charging 3 % commission for selling the flour and 5% for buy.
ing the cotton . H ow many pounds of co tton did he buy ?95. M and N are Jo in t tenan ts of a house , paying
and re spective ly, each quarte r for rent. The land!
AR ITHM ETICAL EXAMPLES. 171
lo rd having raised the annual rent $100, what rent must eachnow pay quarterly ?96 . Having placed a bill of $775 in the hands of a col
lector,who succeeded in obtain ing 75% of i t
,and charged 876
commission,how much did I rece ive
97 . H ow much larger is a square circumscribing a circle40 rods in diameter
,than a square inscribed in the same
circle ?
98. A grocer sold 2000 gallons of molasses for $1880 , andgained on each gallon sold the co st of 137 pints, beer measure . What did the molasse s co st per gallon99. By the fortification bill of 1863
,Congress appropriated
fo r forts as fo llows . Maryland, $200000 ; M ississippi River,
1 7 times as much ; Pacific coast, 22 3o of" the two preceding ap
propriations ; Florida, 1 49— times the three preceding appi opriations ; New York
, 33
3
of the four appropriations alreadymentioned ; and New England 3 3, of all the others. H ow
much was the amount of the bill ?100 . A ’s money was to B ’s as 2 to 3 when A had spen t
$40 , and B had spen t 40% more than A,A ’s money
,minus
$20 was to B ’s money,plus $2 , as 4 to 9. H ow much had
each at first101. A merchan t bought a certain quantity of corn
,for
which he paid a certain sum ofmoney but on measuring,he
found only 3 3 of the quantity he expected. He so ld i t, gaining 3 the cost, and rece ived $2 160, which was at the rate o f
121513cents per bushe l more than he would have paid had he
rece ived the quantity he expected. H ow many bushe ls didhe suppose he had bought
,and at what price
102 . H ow many thousand shingle s,averaging 4 in . w ide
,
and lying 6 inches to the w eather,are required to cover bo th
sides of a roof 3 6 ft. long,who se rafters are 20 fee t in length ?
103 . Andrew Combs purchased 0 3? H . Alexander wheat on3 months credit
,as fo llow s : Apr. 5
,500 bu.
, $ 873 Apr.
172 AR ITHM ETICAL EXAMPLES.
25,3 00 bu.
, $ 95 ; June 20 , 350 bu .
, July 10,
250 bu.
, When was the account due by ave rage ?104 . A, B and C en tered into partnership .
A put in$12000, B $8000 , and C $7000. At the end of the first yearA drew o ut $2000 , B $1000 , and C put in $3 000 .
At theclose of the second year A and B each drew out $1000, andC put in $2000 more. A t the e nd of the third year they disso lved partnership
,and found that the ir jo int property was
$28500 . W hat was each partner’s share ?105. If a pipe 3 inches in diameter discharge 12 hogsheads
of wate r in a certain time,what must b e the diame ter o f a
pipe which w ill discharge 48 hogsheads in the same time ?106. If I buy 50 share s Hudson Rive r R . R . stock at
and 50 share s M ichigan Central R . R . sto ck at the for
mer paying a semi -annual dividend of the latter ofwhat rate of intere st shall I real ize on my investment ?
The horizontal distance b e twe en '
the cave s of a certainbuilding is 40 ft. the elevation of the ridge above the eave sis 15 ft. \Vhat is the length of the rafters108
,I f a man by laboring 15 hours a day do a work in 8
days,how many hours a day must he labor to do the same in
10 days ?109. A speculato r purchased 2553 acre s of land at $453
per acre,but was obliged to se ll i t at $23 3 per acre . For
how much more than his loss did he se ll i t ?110 . What number
,increased by 3, 3 and 3 of i tse lf
,
equals 3 17111 . A w ine dealer de sire s to mix 20 gallons o f w ine ,
w’
orth per. gal .,w ith w ine s w o rth and pe r
gal .,so as to form a mixture of 96 gallons, worth a
gallon . H ow much o f each kind may he take ?112 . J . Smith bought o f Ivi so n ,
Phinn ey , Blak eman Cc .
,
the fo llow ing bills o f goods ; Nov. 1, 186 3 , a bill o f $750 ,on 6
mo .credit ; D ec. 15
,1863
,a bill o f $3 00 , o n 5mo . ; J 1m. 1,
174 AR ITHM ETICAL EXAMPLES .
falo he paid from Buffalo to New Yo rk, 3 and from
New York to Liverpool , Fo r what sum must it b e insured to cover the value of the flour and premium for the
voyage ?12 1 . A man in Cleveland purchased a draft on St. Louis ,
M issouri , for $10640 , drawn at 60 days, payingWhat was the course of exchange ?122 . A merchant sold 350 barre ls of pork for
and gained What did the pork cost him per barre l ?12 3 . A gentleman insure s his house
,w orth $9000, and his
furn iture,worth $3500 , for 3 of the ir value at 375. What
premium did he pay ?124 . I have a circular fie ld 600 rods in circumference.What must be the side of a square field that shall contain thesame area ?125. A’s age i s double that of B
,and B is three times as
old as C,and the sum of the ir age s is 70 . What is the ag e
of each one ?126 . A and B having the same income
,A spends 3 of his .
and B,by spending $200 a year more than A
,finds himself
at the end of 5years $450 in debt. H ow much was theirincome ?127 . Insert 7 geometrical means between 5and 1280 .
128. What sum ofmoney must be invested in 5-20’s,bearing
675 interest in gold, and purchased at to produce a semiannual income of $600 U. S. currency
,gold be ing 1723%
129. A merchan t bought, on 10 mo . credit,25pie ce s of
clo th,each contain ing 3 0 yards , at $46 63 per yard ; after
keeping the goods 3 mo . he so ld them at $5 per yard on acredit of 9 mo . ; money be ing worth what was his ne t
cash gain at the time of the sale ?13 0 . An irregular piece of land contain ing 3 05A. 41 P .
,
was exchanged for a square piece contain ing the same area.What was the length of one of , i ts sides ? If divided in to
b-v w
AR ITHM ETICAL EXAMPLES .
169 square building lots, what w ill be the length of a side o f
each ?13 1 . Bought wheat at and per bushe l .
In what proportion may they be mixed so as to se l l the mixture at $2 153 per bushe l , on 3 mo . credit, when money isworth and make a pre sen t gain of 12%13 2 .
A man purchased a farm fo r $3 000, and agreed to payprincipal and intere st in 4 equal annual installments. Whatwas the annual payment
,intere st being
13 3 . At a certain time betwe en one and two o’clock , theminute hand is be tw e en 2 and 3
,and w ithin an hour the hands
w ill exactly change places. W hat is the first mentionedtime
13 4 . What sum of money, w ith i ts semi-annual dividendsof 4% invested w ith i t, w ill amount to $25000 in 3 years ?135. When gold is quoted at what is the value in
gold of a U. S. note of the denomination of $10 ?13 6 . Account sale s of 100 pipes of gin , re ce i ved per ship
Hispan iola,from Havana
,on 76 of Tyler, Jo ne s, Co.
1860.
Apri l 15 Sold 3 2 Pipes, 4160 gal . at $1 05, on 3 0 days ,M ay 5 40 5240 at 1 .02 , cash,June 28 28 3 650 at
100
CHARGE S.
April 1 To Freight and Primage1 W harfage and Car tagel D uty Bonds , at 60 days
J une 28 Storage from April 1, v iz . :
On 32 Pipe s, 2 w k s . . 64 wk s.
‘ S 40 $ 6 5 6 6. 200
28 13
100 equal to 628 at 60Commission on at 2} per cent 3 34 07
Guaran ty on $43 68 , at 2} per cent 3873 3 2
What are the n e t proceeds of the above account, and whendue ?NGTE —The time for which storage is charged on each part of the
Shipment is the interval,reduced to w eek s, b e tw een Apr. 1
,when the
pipes w ere rece ived into s tore,and the date of sale . E very frac tion of a
week is reckoned a full week .
176 AR ITHMETICAL E XAMPLE S.
13 7 . A walk 9 ft. w ide surrounds a square garden ; thearea of the walk be ing 5of an acre, what is a side of the inclosed square ?13 8. A man in Worcester
,Mass
,has due him in
Chicago . H ow much more w ill he realize by making a draftfor this sum on Chicago
,and sell ing it at discount
,than by
having a draft on Worcester remi tted to him,purchased in
Chicago for this sum at premium?13 9. A father divides an estatew orth between his
two sons,giving the elder 3
5more than the younger. H ow
much is each son ’s share ?140 . M began business w i th $1000 ; four months afte r, S
entered into partnership w ith him,and put in 6 houses
,each
of the same value ; at the close of the year their profits were$3 000, of which S’
s share was $2000 . W hat we re his houseseach valued at ?
A grocer mixed 4 pounds of tea at w i th 3pounds at 1 pound at and 2 pounds atWhat per cen t. profit w il l he make by selling the mixture at
per pound ?
142 . A farme r has sheep worth $4, $6 and $8 a head re
spectively. H ow many of each kind must he sell to realizean average pri ce of a head ?143 . What is the distance from one corner of a cubical
block to the opposite diagonal corner,the side of the cube
being 5 feet ?144 . A and B traded in company . A put in $845for 3 00
days,and received 3 of the gain . The number of dollars
which B put in was equal to the number of days it was em
ployed in trade . What was B ’s capital ?145. Insert 5 arithmetical means be tween 2 and 4 .
146 . If a stack of hay 8 ft. in hight we igh 8 cwt.,what is
the weight of a similar stack that is 24 ft. in hight147 . Allow ing 5% of the hay in the stack last mentioned to
178 AR ITHM ETICAL EXAMPLES .
amount distributed. What 75did they pay ? and how much “
did each creditor rece ive157 . A lo t of land
,containing 15 acre s
,i s 3 0 rods w ide
,
and is a plane incl ining in the dire ction o f i ts length ; one end
be ing 120 feet higher than the other. H ow many acres ofsurface does the inclined plane contain ?158. By selling sugar at $15per cwt. I gain 2075; what 75
should I gain by se lling it at per cwt. ?
159. A man paid annually $10 for’
tobacco from the age of14 until he was 50, when he died, and left $1000 for his he irs.What summight he have left them had he dispensed w i thtobacco
,and loaned the money thus saved at the end of each
year at 6% compound interest160 . Two ships start fromNew York at the same time ;
one sail s due south at the rate of 12 mil es an hour, and theother due east at the rate of 9% miles an hour. H ow farapart are they in 48 hours ?161. A . Banks rece ived a legacy of $3 000 , $800 of which
was payable in 9 months, $800 in one year,and the balance
in two years ; but the executor being w illing to make presentpayment
,discounting at what ought he to rece ive ?
162 .A merchan t rece ives 10000 barrels of flour to sell on
commi ss ion,and is directed to inve st the proceeds in Un ited
State s demand note s bearing interest ; he pays $759charge s
,and sells the Hour at $9 pe r barre l his commission
i s 3 % on the sales . What amount of Treasury Note s can hebuy at 3 6% prem1um, brokerage163 . The fore whee ls of a carriage are 3 ft. 6 in . in diame
ter,and the hind whee l s 4 ft. 9 in . H ow many times must
each revolve in runn ing from Springfield to Chicago, a distance of 204 mile s ?164 . The e xterior diame ter of a spherical she ll is 12 ih . ,
and the she ll is 1 in . thick . What is the difference be tweenthe exterior and interior surface s ?
AR ITHMETICAL EXAMPLES. 179
165. What was the balance of the follow ing account, Jan.
1,1864
,money be ing worthB . NE WTON in account current with J . D AILE Y .
$ 5
s
e
sI 5 II
0
II I
166. What is the pre sent worth of an annuity of $960 inperpetui ty at 6%167 . If 9Z acre s of land are bought for $3 01—3
1 6 ,what w ill
be the co st of 196 3 acre s of land, worth 2 as much per acre ?168. A ball falling from a height of 12 ft. bounds 6 ft. byits elasticity
,and again falling
,bounds 3 ft.
,and so on
,bound
ing each time 5as high as it falls. H ow far w ill the ball fallbefore coming to a state of re st ? and what w i ll be the distance of all the successive bounds169. Fo r what sum must a note be drawn at 3 me . that
the pro ceeds,when discounted at a bank at shall b e
170 . A Cincinnati merchan t bought a quantity of pork for$6000 , and forwarded it to New Yo rk
,paying 975o f the cost
for fre ight and charge s ; it was then so ld by an agent at anadvance of 3 0% on the original co st
,commission H ow
much was the ne t gain ?171 . A broker bought 90 shares of $100 each of New York
Central R . R . stock at and so ld the same atHow much was the ne t gain ?172 . A circular cistern 7 ft. in diame ter has a capacity o f
gallons . What is its depth ?173 . H ow many pupils in a schoo l when attend the gram
mar department, the intermediate,and the remainder
,
which i s 3 4 le ss than }z the who le numbe r of scho lars,attend
the primary174 . A man insured his house
,valued at $18000, and fur
180 AR ITHM ETICA L EXAMPLES.
niture,worth $7000 , for {g of the ir value , .
at m. Whatpremium did he pay175. H and J traded in company ; H put in $8000, and J
$20000 they were to share the gain s or losse s equally at theend of two years they dissolved partnership
,and found the ir
ne t capital to be $22500 . What was each one’s share ?176 . A person exchanged 180 share s of 6 per cen t. stocks,
at for 10 per cen t. stocks,at H ow much was his
yearly income increased177 . I f a man dig a square cellar that measures 5 ft. each
way in one day,how long w ill i t take him to dig one meas
uring 10 ft. each way ?178 . Sold coffe e at 13 ; cents a pound, and the reby lo st 20§é
on the co st ; afterward so ld a quantity of the same for $455,and gained 3 054. What quan tity was sold ? and at whatprice179. The diameter of the sun i s 1 10 times as large as that
of the earth . The volume of the sun i s how many times aslarge as the vo lume of the earth180. Received an invoice of crockery
,5per cent. of which
was broken ; paid a duty o f 20 per cent. upon the remainder.
For what per cent. above the invo iced value must it b e soldto gain 25per cen t. on the who le co st ?181. The length of a rectangular field contain ing 13 A. 3 R .
5P . i s to its breadth as 9 to 5. What are its dimensions ?182 . Amerchan t in New York in 1863 gave $5044 .72 fgf or
a bill of exchange on London for £650 . What was the rateof exchange183 . A gentleman laid out a garden in the form of an
e llipse,i ts longer d iameter be ing 8 rods
,and i ts shorter 5
rods. What was the area of the garden ?184 . If stock
,bought at 20% premium,
pay 63 5on theinvestmen t
,what w ill it pay if bought at discount ?
185. H ow many yards of plastering in a room 2 1 ft. 9 in.
182 ARITHMETICAL EXAMPLES .
$24500 . In ferest no t be ing reckoned on receipts and ex
pe nditures, how much must L pay to A andW ?
194 . The contents of a cubical block of granite are 49 13solid feet. What are the superficial contents ?195. A offers to loan to B $1000 for 6 mo .
,at the
legal rate is 7 For what summust the note be drawn thatthe amount of it at 7% w i ll equal the amount of $1000 at 10%for the given time ?196 . The duty at 3 0% on a quantity of coffe e in bags
,each
w eighing 175pounds gro ss,and invoice d at $ 14 a pound ,
was Tare being how many bags w ere im
ported ?197. A father divided his property among his four sons,
directing that A should have $6 as often as B $5, C $3 as
often as A $4 , and D $8 as often as B $9. What was theamount of property
,D ’s share being $6000 ?
198 . J . Ell is (St Co . sold Thomas Strong goods to the
amount of $2500, on 6 months’ credit ; Strong paid $350 in2 months
, $600 in 4 months , $500 in 7 months , and the balance in 12 months. W hat amount was due at the time ‘ofsettlemen t
,interest 7
199 . What in advance of the cost must a merchantmark his goods so that
,allow ing 4% of his sales for bad debts,
an average credit of 3 months,and 8% of the cost of the goods
forexpenses,his ne t gain may be 15% of the first cost of the
goods,money being worth 7%
200 . \Vhat is'
the present w orth o f an annuity of $1200 in
reversion 7 years,and continuing 13 years
,at 6%
20 1 . The perpendicular he ight of-a con ical glass is 8 inand its diame ter at the top is 5 in . H ow much water w ill ithold202 . What costs a bill on London for £800 17s . 6d.
,when
the rate of exchange is 9g% premium203 . A miller grinds 500 bushe ls of provender, worth 75
ARITHMETICAL EXAMPLES . 183
cents a bushel,from 40 bushels of rye , worth 90 eents , a
bushe l,and from oats worth 60 cen ts, corn w orth 85 cents,
and barley worth 80 cents a bushe l . H ow many bushe l s ofcats
,corn
,and barley may he take ?
204 . A gentleman purchased an annuity of $1000 , to continue 20 years
,a t 673, compound interest. What did it cost
him
205. A and B engage in trade ; A puts in $10000 , and at
the end of 5 months takes out a certain sum ; B puts in$6000, and after 3 months puts in $4000 more ; at the end of
the year,A’s gain is $1800 , and B ’s $2250 . What sum did
A w i thdraw at the end of 5months ?206 . A merchan t sold 48 yards of gingham at
' centsper yard
,12 pieces of sheeting
,each co ntain ing 3 3 yards
,at
25 cents per yard,and received in paymen t 40 bushe l s of
cats at cents pe r bushe l , and the balance in money.
H ow much money did he rece ive ?207 . If the interest of for 1 mo . 3 da. i s $3 167 ,
what w ill be the interest of fo r 10 mo . 26 da.,at
tw ice the rate ?208 . S. F. Root bought 50 Share s of bank stock at an ad
vance of 5% on the par value of $100 . From the time ofpurchase until the end of 3 yr . 9 mo . he rece ived a semi-annual dividend of whenhe so ld the sto ck at a premiumof Money be ing compound interest
,how much did
he gain ?209. My garden i s 11 rods 7 7} fe e t long, and 9 rods 15 1
fe e t w ide . What is the length of the longe st rails that can b eused in fencing it
,allow ing the end of each rail to lap by the
o ther 5 in .,and all the panels to b e of equal length ? H ow
many rails w ill fence the garden,i f 6 rails are allowed to
each pane l ?2 10 . If 4096 men are formed into an oblong
,w ith 4 time s
as many men in rank as in file,how many w ill there b e in
rank and file ?
184 ARITHM E TICAL EXAMPL E S .
2 11. A gentleman purchases a farm for $10000, which hese ll s after a certain number of years for $1407 1, making on
the inve stment 5% compound intere st. He now inve sts hismoney in a perpe tuity
,which is in reversion 11 years from
the date of purchasing the farm. Allow ing 6% compoundinterest for the use of monev, find the annuity and the lengthof time he owns the farm.
2 12 . Three numbers are to each other as 3,5and 7
,and
their con tinued product is 2835. Required the numbers .2 13 . W hat sum must b e inve sted in 8 per cent. stocks, atto produce an annual income of $2000 ?
2 14 . The shadow of a steeple measured 8 rd . 3 yd . 1 ft.
and 6 in . in length,at the same time when the shadow of a
man 6 ft. high measured 4 ft. 9 in . Required the he ight ofthe steeple .2 15. J. Smith owes C. Brown $2000 , to b e paid in equalannual payments of $400 each ; Smi th, no t be ing able to mee tthese payments at their maturities
,and having an estate 12
years in reversion,arrange s w i th Brown to wait t ill he enters
upon his estate,when he i s to pay him the who le sum w i th
compound interest at What sumw ill Brown then re
ce ive
2 16 . J . Clarke bought of Claflin Mellen the fo llow ing b n lof goods : June 1
,a bil l of $650, on 4 mon ths ; Sept . 15
, abill of $800 , on 3 mon ths ; Oct. 10 , a bill of $1200, on 1
month. What was the equated t ime of payment ?
2 17 . If a cable 3 inche s in d iame te r w ill sustain a w e ighto f 18000 pounds
,what w e ight can b e sustained by a cable
inche s in circumference ?2 18 . Divide $2000 between A and B
,so that A’s money
shall be of B ’s.2 19 . An estate o f $60000 was to b e divided among a w ife ,
son and two daughte rs,as fo llows : The w ife was to have
$5000 more than the son,the son $10000 more than the e lder
186 ARITHMETICAL EXAMPLES.
men $1 a week, and to the boys $3} a we ek . How manywere there of each ?229. A and B traded together ; A put in $540 for 480days
,and rece ived 5of the gain ; and the. number of do llars
which B put in was equal to the number of days it was em
ployed in trade. What was B ’s capital ?23 0 . What is the present value of a reversionary lease o f
$100, commencing 14 years hen ce,and to continue 20 years
,
compound interest at 5per cent .23 1. If a cistern 6 feet in diameter hold 80 barrels of water
,what must be the diameter of a cistern of the same depth
to ho ld 1280 barrels ?2 3 2 . A gentleman in Boston drew on W urtemb erg for
6000 gilders at $ 415per gilder. H ow much mo re would hehave received if he had ordered remittance to London
,and
thence to New Yo rk,exchange at W urtemb erg on London
be ing gilders per £1,and at London o n New York
in favor of sterl ing,brokerage at lgfi in London for re
mitting2 3 3 . Two boys, each 12 years old, have certain sums ofmoney left to them ; the sum left to one i s put out at 773simple intere st
,the sum left the other at 673 compound inter
est,compounded semi-annually
,and the amoun t of each boy ’s
money w ill be $2000 when he is 2 1 years old. W hat is thesum left to each boy23 4 . Find the sum of 2 1 terms of the serie s 5
,4g, etc.
2 35. A man trave led 13 days ; his last day s journey was80 mile s
,and each day he traveled 5mile s more than on the
preceding day. H ow far did he travel,and what was his first
day ’s journey ?2 3 6 . Find the 12 th term of the series
,3 0
,15
,75, e tc.
2 3 7 . Bought 12 yards of clo th fo r $15. H ow many yardsmust I buy at $1§ and $43 a yard, that the average price ofthe whole may be $lg
5
ARITHMETICAL EXAMPLES. 187
23 8. A man bequeathed his prope rty,amoun ting to $3 0000 ,
to his w ife and three children as fo llows : The w ife was to
have and the remainder was to be divided so that the share so f the children at simple intere st at 6% Should all amount tothe same sum when they were 18 years bld ; the ages of thechildren w ere respectively 4 yr .
,5 yr. 6 mo .
,and 7 yr. 3 me .
What was the share of each child ?23 9. What summust b e inve sted in Un ited States 10-40
’s,
bearing 5% interest, payable in gold, purchased at par, to produce a semi-annual income of $400 U . S. currency
,when gold
is quoted at240 . Imported 12 casks of wme
,each contain ing 42 gallons
invoiced at per gallon paid $96 for freight, and a dutyof H ow much shall I gain in sell ing the whole for
24 1 . H . Derby contracted to dig a trench 1000 yd . long,in
24 days. Having employed 54 men for 15 days,he found
that only 450 yd . had been dug. H ow many more men musthe employ to fin ish the trench according to the contract ?242 . The duty of a garrison
,consisting of 5 compan ies
,
containing respective ly 40,50
,60
,70 and 80 men
,requires
90 men each day . What number must each company fi1r
n ish ?243 ° $750 ' M ID D LEFIE LD
, Sept. 1 , 1858.
Six months after date I promise to pay H . Harger or order,seven hundred fifty dollars
,for value received, w i th intere st.
J OHN J OSLYN.
Indorsed as follows :March 1, 1859, $200 ; June 16 , 1859,$100 ; Jan . 1, 1860 , $225. What was due Oct . 19, 1862 ?
244. The duty on an invo ice of 3 00 dozen London porter,at was breakage
,Required the invoiced
price per dozen .
245. In how many differen t ways may the letters of thealphabe t be arranged, taking 15 each time ?
188 ARITHMETICAL EXAMPLES.
246 . What is the equated time for paying the balance of
the following account ?J. J ONE S
,in accoun t with B . D AY .
247 . H ow much sugar,at 4
,5 and 9 cents a pound
,must
be mixed w i th 72 pounds at 12 cents a pound, so that themixture may be worth 8 cents a pound ?248. Insert four arithmetical means between 2 and 79.
249. A person w ishes to discharge a debt Of $1125 in 18
annual payments,which shall increase in ar i thme tical pro
gression . H ow much must his first payment be in order thatthe last may be 120 ?250 . Three merchants have an interest in a steam vessel ;
A puts in $960 for six months ; B , a sum unknown , for 12months ; C, $640 for a time not known when the accountswere settled ; A ,
received $1200 for his share, stock and
profit ; B , $2400 for his, and C, $1040 for his. What wasB ’s stock
,and C’s time ?
251. In the foregoing question A’s gain was $240 during6 months ; B ’s
, $800' during 12 months
,and C’s
, $400 during15months
,and the sum of the products of their sto cks and
times was 3 4560 . What were their stocks252 . In the same question the sum of the stocks is $3 200 ;
A’s stock was in trade 6 months ; B ’s,12 mon ths
,and C’s
,15
months ; at the se ttling of accounts, A is paid $240 of thegain ; B, $800 , and C, $400 . What was each person ’s stock ?253 . A man bought a piece Of prope rty fo r $10500 , and
agreed to pay principal and in tere st in 3 equal annual installments. H ow much was the annual payment, intere st being775?
2 ROBINSON’
S SERIES OFMATHEMATICS.
Particular attention has b e en given to the preparation of
.
thosesubj e c ts , which are abso lute ly e ssen t ial to make good accountants
and comme rcial bus in ess men .
The differe nt kinds of U n ited State s Securi ties are describ ed, the
diffe re nc e be twe en gold and currency, and the cc rre spondingdiffe re ncein price s exhib ited in trade , are taught and i llus trated ; also , a full
Treatise o f the M e tric System of W e ights and M easures has beenadded.
A r i thme ti cal E x amp le s . Thi s book contain snearly Practical E xamples , promiscuously arranged, and
w i thout the answe rs give n , involving nearly all the principlesand ordinary processes o f common arithme tic, de signed tho
roughlyto test the pupil’s j udgmen t ; to cultivate hab i ts o f pati entinvestigation and self reliance ; to te st the truth and accuracy o fhis own proce sses by proo f ; in aword , to make him i ndependent
of a tex t-book , w r itten r ules and analys is .
This work is no t de signed fo r b eginners , but for those who haveacquired at least a partial knowledge o f the theory and applicati onso f numbe rs from some o the r work , and i t may b e used in conne c ti onw ith any o the r book , or Se ries o f books on this subj ect, for R evi ewo r D rill E xe rcises .A n edi tion is printed ex clus ively for teachers , containing the
answers at the close o f the book .
lVew E leme n tar y A lg e b ra : a clear and practi calTreatise adapted to the comprehension of b eginners in the
Science . The introductory chapte r i s designed to give the
pupi l a correct comprehe nsion o f the utili ty of symb ols , and of
the ide ntity and chain of connection b e twe en A rithmetic andA lgeb ra, leading him by easy and succe ssive steps , from the studyof written arithmetic to the s tudy o f mental and wri tten algebra.
N ew U n i ve r s i ty A lg e b ra ,con tain ing many n ew and
original Me thods and Applications b o th o f Theory and Practice ,and i s des igned for H igh Schools and Colleges .Th is b ook is not a r ev ision , but a newly prepared and recently
publ i she d wo rk , thoroughly sc ie nt ific and practi cal in i ts di scussi onsand applic
ations . It is a book filled with gems , andmo st o f themoriginal wi th the author.
ROBINSON'
S SERIES OFMATHEMATICS.
,In i t w ill b e found condensed and b ri e f modes of operation , not
hithe rto much k nown o r ge ne rally prac ticed,and se ve ral expedients
are sys tematized and taught , by which many o the rwis e tediousope rations are avmdedB re vi ty and pe rspicui ty, two rare and commendatory ex ce llence s
in a tex t-book , are leadi ng features to this work , and, at the samet ime , the rationale o f eve ry Ope ration , and the foundati on of eve ryprinc iple , are fully and clearly shown .
The design throughout has b e e n , not to conceal, but fully to r eveal
the difficulti es o f the science , and to encourage the learner, no t toavo id, but to grapple w ith, and to ove rcome them; sin ce , to the
student o f Mathematics labor rightly dire cted, is discip line , anddiscipline , afte r all, i s the true end o f education .
New Ge ome tr y an d Tr i gon ome tr y , embracingPlane and So lid Ge ome try, and Plane and Spherical Trigo nometry, with numerous practical Problems , the whole newlyillustrated. New and original demonstrations of some o f the
more important principles have b e en given , and the practicalproblems and applicat ions , b o th in the Geome try and the Trigonome try, have b e en g
r eatly increased.
N e w Su rv ey i n g a n d Nav igati on . W'
th use o f
Instrume nts , e sse ntial E lements Of Trigonome try, M e nsuration ,
and the necessary Tables , for Schools , Colleges, and PracticalSurw yors .
The arrangement o f the work , including as i t do es Trigonometryand M ensurat i on , requires that two terms should b e employed in i tscomple tion , but stude nts familiar w ith the se subj ects , by omi ttingthem, can readily master the subj ect o f Surveying preper in one
term.
N ew Co n i c Se c ti o n s an d A n a ly ti ca l Ge ome tr y
- prepare d fo r High Schoo ls and Co lleges.
N ew D ifi‘
e r e n ti al an d In teg ra l Ca lcu lu s
adapted for use in the H igh Schools and Co lleges o f the country
thorough and compr ehens ive in its characte r ; and while it do esnot cove r the whole ground of this branch of Mathematics , ye tSO far as the subj ect is treated, i t is p rogr essive and complete .
It is confidently b eli eved that in li terary and scientific merit,
this wo rk is not equalled by any similar production published in thiscountry.
ROBINSON'
S SERIES OFMATHEMATICS.
K i dd le ’s N E W M an u a l of th e E lemen ts of
”
A s tr o n omy . Compri sin g the latest d i sco ve ries andtheore t ic vie ws , wi th directions for the use Of the Globes ,and forstudying the Constellations .
The Publishe rs offe r this work to accompany “ ROBINSON’
SMATHE MATICAL SE RIE S.
”
The p lan o f the wo rk 18 obj ective ; the i llustrations are new and
cop io us ; the methods greatly s implified ; the n umer ical calcu
lal i'
o ns , wh1ch are based on the recen t de termination of the Solarparallax , are made wi thout recourse to any o ther than E lementaryA r ithmetic, and the most r udimental p r inciples of GeometryThe b ook is designed fo r use in NORMAL SCHOOLS, A CAD EMIE S,
H IGH SCHOOLS, SE MINARIE S, and advanced classes in GR AMMARSCHOOLS ; and i t i s h oped that in this work the thorough and prac
t icalTeacher w ill find a des ideratum long sought for in this department o f scie nce .
U n i ve r s i ty A s tr o n omy. Descriptive, M athematical , Theo re tical and Physical ; designed for H igh Schools andColleges . Large 8vo
N e w Ge ome try , b ound separate, in cloth.
P lan e an d Sp h e r i ca l Tr i go n ome try, in separate volume , clo th .
Co n c i s e M a th ema ti ca l Op e rati on s . B eing a
Sequel to the author ’s Class-books , withmuch additional matter.
K ey to Ge ome try an d Tr i go n ome try , Su r
v eyi n g an d N av i ga ti o n .
K ey to A n a ly ti ca l Ge ome try , D iff e r en ti alan d In teg ra l Ca lcu lu s , w ith some additionalA s tronomical Problems in the same volume .
K eys to th e A r i thme ti cs an d A lg e bras , are
.published for the use Of Teachers .
metiran fihumfi
P U B LI SH E D B Y
IVISON , PHI N NEY, BLAKEMAN
47 a: 49 Gu amSTREET, N. Y.
Q
ROB INSON’S M l
‘t'
l‘
llE MATlCAL SE RIE S.
KE Y TO PRACTICAL .s fi n flJ f l fl
PR OGR E SS TE HIGH ER
KE‘
Y TO NE W E Lmu. Lu Y M‘
GE B ie’
rfii
KE‘
Y TO UNIVE R SITY ALGE BRANE W UNIVE RSITY ALGufi H/ l,
ANAL YTICAL 0 13 0a It AND coma SE CTIONS,
D IFFE RENTIAL AND INTE GRAL'
CAL CULUS,-
(IN PRESS)
CONC'ISE MATIIE'JIA N th/l l"; OPE RATIONS,
W The most a 1 terms j onfimt supplies , f or in