Section 3.2 – Problem Solving

Number Problems

Numbers The sum of two numbers is 25. The difference of two numbers is 3. Find the numbers.

number second

numberfirst

y

x

3

25y

yx

x

14

282

x

x

11

2514

y

y

11number second

14numberfirst

y

xUse Elimination

Number Problems

Numbers Juan is thinking of two numbers. He says that 3 times the first number minus the second number is 118. In addition, two times the first number plus the second number is 147. Find the numbers.

number second

numberfirst

y

x

1472

118y3

yx

x

53

2655

x

x

y

y

y

41

118159

118)53(3

41number second

53numberfirst

y

xUse Elimination

Revenue and Cost

Revenue Let represent a company’s revenue, let represent the company’s cost, and let x represent the number of units produced and sold each day. Find the company’s break-even point; that is, find x so that R = C.

xxR 16)( 36457)( xxC

36457)(

16)(

xxC

xxR

3645716

)()(

xx

xCxR

36459 x

405x units 405x

Use Substitution

Perimeter

Perimeter The perimeter of a rectangle is 260 centimeters. If the width of the rectangle is 15 centimeters less than the length, what are the dimensions of the rectangle?

width

length

y

x

15

260

xy

yyxx

15

26022

xy

yx5.72

2904

260304

2603022

260)15(22

x

x

x

xx

xx

cm 57.5 width

cm 72.5length

y

x

5.57

155.72

y

yUse Substitution

MixturesInvestments Marge and Homer have $80,000 to invest. Their financial advisor has recommended that they diversify by placing some of the money in stocks and some in bonds. Based upon current market conditions, he has recommended that three times the amount in bonds should equal two times the amount invested in stocks. How much should be invested in stocks? How much should be invested in bonds?

bonds in investedamount

stocks in investedamount

y

x

xy

yx

23

80000

yx 80000160000

21600003

)80000(23

y

yy

yy 32000

1600005

21600003

)80000(23

y

y

yy

yy

48000

8000032000

x

x

000,32$bonds in investedamount

000,48$stocks in investedamount

y

x

Use Substitution

MixturesCandy A candy store sells chocolate-covered almonds for $6.50 per pound and chocolate-covered peanuts for $4.00 per pound. The manager decides to make a bridge mix that combines the almonds with the peanuts. She wants the bridge mix to sell for $6.00 per pound, and there should be no loss in revenue from selling the bridge mix versus the almonds and peanuts alone. How many pounds of chocolate-covered almonds and chocolate-covered peanuts are required to create 50 pounds of bridge mix?

peanuts pounds #

almonds pounds #

y

x

)50(00.600.450.6

50

yx

yx

yx 50

10

2550.2

30050.2325

300450.6325

3004)50(50.6

y

y

y

yy

yy

40

5010

x

x

Use Substitution

300450.6

50

yx

yx

lbs 10peanuts pounds #

lbs 40almonds pounds #

y

x