math problem solving vol2 - it.iitb.ac.in

Teacher Workbooks

Mathematics Series Problem Solving – Vol. 2

© Copyright 2003 Teachnology Publishing Company A Division of Teachnology, Inc. For additional information, visit us at www.teach-nology.com/publishing

© 2003 Teachnology, Inc. iii

Table of Contents Mathematics Problem Solving Word Problems 1-30

Standard

National Mathematics Content Standard: Problem Solving for Grades 3-5 1-30

Name _______________________________ Date __________________________ Math- Problem Solving with written explanation.

National Mathematics Content Standard: Problem Solving for Grades 3-5 © 2003 Teachnology, Inc.

1

Directions: Read through the following information. Answer each question thoroughly. Remember to answer in complete sentences when necessary. Show and label all of your work and answers. Use the back of this paper if you need more work space.

1. An amusement part charges $0.75 a ride. The park also sells a coupon book for $15.00 that provides tickets for 25 rides. How much money does purchasing the coupon booklet save? Explain your answer.

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2. A new washing machine cost $342.39 on sale. If the store held a 20% off sale, what was

the original cost of the machine? Explain how you arrived at your answer.

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3. Theatre tickets went on sale for $89.00. Each ticket carried an additional $12.50 charge.

If a group of 14 people ordered tickets, what was the total cost? Explain how you arrived at your answer.

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2


1. The cost of a new video game cartridge is $22.99. If the store is having a 40% off sale, what is the new price of the cartridge? Explain how you arrived at your answer.

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2. If 63,852 seeds were planted in 12 equal rows, how many seeds were planted in each

row? Explain your answer.

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3. Linda’s water bill was $82.00 each 3 months. What did Linda pay in one year? Explain

your answer.

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3


1. Sweet gourmet chocolates cost $2.75 per pound. How much does 19.5 pounds cost? Explain your answer.

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2. Tom bought 24 gallons of outdoor paint. One gallon cost $18.68. The store was having a

10% off sale. How much did Tom pay for all 24 gallons? Explain your answer.

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3. Danielle’s phone bill was $264.88 this month. She wants to reduce her phone bill by at

least 50%. What is 50% of her current phone bill? Explain your answer.

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4


1. Rosalyn walks around the local high school track every evening 10 times. The track is a ¼ mile track. How far does Rosalyn walk? Explain how you arrived at your answer.

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2. Ben rode his bike 4 miles each day for one year. What was the total distance he traveled?

Explain your answer.

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3. The temperature in the Antarctic can be as low as –128.6 degrees Fahrenheit. The

average inland temperature is about -94 degrees Fahrenheit. What is the difference between the lowest and average temperature in the Antarctic? Explain your answer.

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5


1. A puppy is 4 days, 16 hours, 46 minutes old. How many minutes old is the puppy? Explain your answer.

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2. A bike ride took 3 hours and 36 minutes to complete. What was the average speed of the

bicyclist if the total distance traveled was 55 miles? Explain your answer.

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3. The length of the primary hallway is 47 feet. The intermediate hallway is 14 feet longer.

What is the length of the intermediate hallway? Explain your answer.

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6


1. Mrs. Newberry drove 17 miles, in one direction, each day to work. She works Monday through Friday. What is the total distance Mrs. Newberry drives in one week? Explain your answer.

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2. A round trip ferry ride is 5.8 miles. If Andy rides the ferry every day of the week, how far

did he travel in one week? Explain how you arrived at your answer.

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3. RJ walked 2 miles every other day for 30 days. How far did RJ walk? Explain your

answer.

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7


1. Henry wanted to purchase a truck for $21,760.99. Henry had to borrow $15,000.00 from the dealership. If Henry paid the dealer by the end of the year, he only would have to pay 3.7% in interest. How much interest will this be for the one year? Explain your answer.

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2. The cost of a dinner was $43.85. Tax was not included. What was the total bill if a 7¼%

tax was added? Explain your answer.

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3. One pound of candy cost $5.99. How much will 6 pounds cost? Explain your answer.

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8


1. A sandwich order was called into a local deli. One sandwich came to $3.59, another $4.96, a third $6.36, and a fourth sandwich came to $2.50. Each price included tax. What was the total bill? Explain your answer.

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2. A new pair of roller blades cost $73.99 at store one. The same pair of blades was on sale

for $64.79 at store two. How much money is saved if the blades are purchased at store two? Explain your answer.

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3. Mike’s favorite cereal costs $4.59. His mom bought 26 boxes this past year. How much

was spent on his cereal? Explain your answer.

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9


1. Each bag of dog food weighs 32 pounds. If Matt carried a total amount of 384 pounds, how many bags did he carry? Explain your answer.

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2. Two hundred six bags of mulch were needed to cover a large garden. Each bag weighed

12 pounds. What is the total amount of weight of the bags? Explain your answer.

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___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 3. A total of 75,600 pounds of dirt was needed to fill a hole. Each truckload could carry 2,700 pounds. How many truckloads were needed? Explain your answer.

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10


1. Eighty-seven stitches are needed for one row in a blanket. The blanket is made up of 1,683 rows. How many total stitches were included in the making of the blanket? Explain your answer.

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2. Six thousand forty two fans attended a ball game. Only four thousand ninety five fans

attended the next game. How many more fans attended the first game? Explain your answer.

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3. A sandwich with 5 sides (cheese, lettuce, tomato, etc.) costs $3.99 at the local deli. The

neighboring convenient store sells the same sandwich for $3.00 and charges $0.25 per sides. Which place has the better deal if all 5 sides are included? Explain your answer.

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11


1. Catherine played bridge for 3 hours on Monday, another 3.5 hours on Wednesday, and 3.5 hours more on Friday. How long did Catherine play bridge for during this week? Explain your answer.

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2. Janet also plays bridge. She spent 7 hours the first week of a month playing, 10 hours the

second week, 7 hours the third week, and another 8 hours the fourth week. What is the average amount of time Janet spent playing bridge this month? Explain how you arrived at your answer.

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3. Bob likes to paint. In February, he spent a total of 42 hours painting. How long did Bob

paint each day of the month? Explain how you arrived at your answer.

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12


1. Sara received the following grades on her spelling tests: 96%, 88%, 100%, and 84%.

What was her average? Explain your answer.

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2. Corrine had 3 math tests this month. She scored a 75%, 84%, and 90%. What was her

math average this month? Explain your answer.

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3. Kyle spent $4.89 on new socks and another $75.47 on other articles of clothing. How

much did he spend in all? Explain your answer.

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13


1. The average speed of a vehicle is 63 mph. How far did this vehicle travel if it continued at that speed for 4 ½ hours? Explain your answer.

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2. A plane traveled 2,773 miles in 6 hours. What was the plane’s average speed? Explain

your answer.

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3. Pat drives 24 miles each direction to work. It takes Pat 40 minutes to get to work. What is

her average speed driving to work? Explain your answer.

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14


1. Each weekend, Linda spends time in her garden. She spent 12 hours working in the garden on each of the four weekends during the month of July How much total time did Linda spend in her garden during this month? Explain your answer.

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2. Emily likes to spend as much time as she can outdoors. She spent 30 minutes on Monday,

15 minutes on Tuesday, 45 minutes on Wednesday, 95 minutes on Thursday, and 25 minutes on Friday. What was the average amount of time Emily spent outdoors each day during this week? Explain your answer.

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3. Tom’s reading assignment is to read 920 pages over the next twenty days. How many

pages will he need to read each day to complete the assignment? Explain your answer.

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15


1. Anna spends 15% of her day helping her elderly parents. Another 5% is spent exercising. How much time does she spend doing these two activities? Explain your answer. (Hint: one day equals 24 hours.)

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2. Lisa commutes 45 minutes in each direction to work. How much time does she spend

commuting in one business week? Explain your answer.

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3. The distance to Richard’s summer home is 295 miles. If the average speed traveled to

this location was 59 mph, how long did it take to get there? Explain your answer.

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16


1. Scott received the following 6 grades this quarter in Science: 86%, 97%, 69%, 83%, 91%, and 78%. What was his average? Explain how you arrived at your answer.

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2. A state trooper clocked the speed of 7 vehicles on the highway. They were 58 mph, 79

mph, 65 mph, 87 mph, 55 mph, 60 mph, and 58 mph. What is the average speed of these? Explain your answer.

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3. The temperature Tuesday through Friday ranged from 85 degrees Fahrenheit on Tuesday,

56 degrees on Wednesday, 65 degrees Fahrenheit on Thursday, and 60 degrees Fahrenheit on Friday. What was the average temperature between Tuesday and Friday? Explain your answer.

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17


1. Dominick works from seven thirty in the morning until four in the afternoon Monday through Friday. He is away from his home during this time. How much time is Dominick out of the house during the week? Explain your answer.

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2. Jack spends 30% of each day in the office. How many hours is Jack at the office? Explain

your answer. (Hint: one day equals 24 hours.)

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3. John’s phone bill was $39.76 in March, $62.38 in April, and $42.79 in May. What was

the average phone bill for these three months? Explain your answer.

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18


1. Anna loves to horseback ride. She spends an average of 10% of each day at the stable. How much time does Anna spend at the stable? Explain your answer. (Hint: one day equals 24 hours.)

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2. Josh and his sister Teri spent $200.00 on a new printer. They also spent a total of $132.48

on accessories for the printer. How much did they each pay if they split the cost evenly? Explain your answer.

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3. Four friends went in equally on the purchase of a small Cessna airplane. How much did

each person contribute if the total cost of the aircraft was $11,056.00? Explain your answer.

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19


1. Chris ran 219 days in one year. What percent of the year did he run? Explain your answer.

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2. Mark counted 726 red M&Ms out of a total of 1320 M&Ms. What percent of M&Ms

were red? Explain your answer.

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3. Using the numerical information from #2, what percent of M&Ms were other colors?

Explain your answer.

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20


1. Anthony drove cross-country. He totaled 3,395 miles. He tallied 338.6 miles as necessity miles, such as stopping for gas and lodging. What percent of mileage was spent sightseeing? Explain your answer.

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2. A painter spends 15% of their time scraping, 75% of their time painting and the

remaining time shopping for materials and travel time. What percentage of total time does the painter spend traveling and shopping for materials? Explain your answer.

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3. A cab ride lasted 45 minutes. Eighteen percent of that time was spend sitting in traffic.

How much time was spent not moving? Explain your answer.

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21


1. The sun shone for 10 hours 48 minutes on Friday. What percent of the day was spent in daylight? Explain your answer.

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2. Luke’s car had 56,831 miles on the speedometer. Seventy five percent of those miles

were from highway driving. How many miles were spent driving on the highway? Explain your answer.

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3. Marybeth swims for 1.5 hours every other day. How much time would Marybeth spend

swimming in the month of April? Explain your answer.

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22


1. The distance from point A to point B is 36 times the length of the line below when measured in inches. What is the distance from point A to point B? Explain your answer.

A ________________________________ B

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2. What is 50% of the distance of the following line, measured in centimeters? Explain your

answer. __________________________________________________________________

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3. What is 482 times the length of the line below, measured in inches? Explain your answer.

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23


1. Only ¾ of the entire team ate meat. The remaining members were vegetarians. The team has 44 members. How many of them eat meat? Explain how you arrived at your answer.

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2. One fifth of the choir was unable to attend the parade. The choir has 575 members. How

many choir members were unable to sing in the parade? Explain your answer.

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3. During a boat ride, 30% of the time was spent in daylight. The remainder of the time was

in darkness. The ride was 2.5 hours long. How much of the boat ride was in daylight? Explain how you arrived at your answer.

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24


1. Sarah has 3/5ths of her school project complete. What percent of her work is complete? Explain your answer.

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2. Elaine has ridden 17 miles of a 25-mile bike ride. What percentage of the ride has she

completed? Explain your answer.

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3. A popular clothing company has added 54 new stores around the world. In the first

month, ½ of the new stores added a new clothing line. How many stores increase their inventory? Explain your answer.

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25


1. Saul usually places mail in six hundred and sixty mailboxes each day. His route is reduced 3 times a week by 25%. How many mailboxes does he deliver mail to when his route is reduced? Explain your answer.

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2. Mike spent ¾ of his summer on out of town on vacation. He had 64 days off from school.

How many days was Mike out of town? Explain your answer.

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3. Four thousand six hundred eight five vehicles passed over a bridge in one morning. Two

tenths of the vehicles were busses. How many busses crossed the bridge this day? Explain your answer.

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26


1. Four tenths of the fifth grade has turned 11 years old. There are 115 students in the 5th grade. How many students are 11 years old? Explain your answer.

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2. The local oil change shop averages 140 cars a day. Three fifths of the vehicles are sedans.

How many vehicles are sedans? Explain your answer.

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3. An elementary schools total student enrollment is 1,325. One fifth of the students are

fourth grader students. How many of the students are fourth graders? Explain your answer.

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27


1. Four hundred fifty six flights depart from the airport each day. Three eighths of the flights head toward warmer weather locations. How many flights travel toward a warmer place?

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___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ ___________________________________________________________________________ 2. One fifth of the fourth grade class went on summer vacation out of state. There are 125

students in the fifth grade. How many students vacationed out of state? Explain your answer.

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3. A ride that usually takes 5 hours took 8 hours due to weather and traffic. How much

longer was the ride? Explain your answer.

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28


1. Jack is awake almost 16 hours of each day. What fraction of time in each day is he awake? Explain your answer.

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2. Elijah spent 17 days in Europe during the month of September. What fraction of time in

September did he spend in the Europe? Explain your answer.

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3. Ryan spends 3 hours each day working on theatre directing. What fraction of his day is

spent on theatre work? Explain your answer.

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29


1. Lauren traveled 164 miles round trip four times during the year. How far did she travel in all? Explain your answer.

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2. Kara spent 2.5 hours every other day for sixty days studying the French language. How

much time did she spend learning the language? Explain how you arrived at your answer.

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3. A trip to visit relatives up north totaled 386 miles. To visit relatives in the south required

a 539 mile road trip. The trip up north is how much shorter than the trip south? Explain your answer.

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30


1. Scott ran 3.2 miles each day for 25 days. What was the total distance he ran? Explain your answer.

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2. A movie theater had 30 rows with 25 seats in each row. How many people could the

theater hold? Explain how you arrived at your answer.

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3. Lou rode his exercise bike 5 out of 7 days per week for 52 weeks. He rode 30 minutes

each time. How many minutes in all did Lou ride the bike in one year? Explain how you arrived at your answer.

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© 2003 Teachnology, Inc. 31

Answers Page 1 1. $3.75 saving: .75 x 25; $18.75 - $15.00 2. $427.99: $342.39/4 = $85.60; $342.39 +

$85.60 3. $1,421.00: $89.00 + $12.50 = $101.50 x 14 Page 2 1. $13.79: $22.99 x .40 = $9.20; $13.79 - $9.20 2. 5,321 seeds: 63,852/12 3. $328.00: $82.00 x 4 Page 3 1. $53.63: $2.75 x 19.5 2. $403.49: $18.68 x 24 = $448.32 x .10 =

$44.83; $448.32 - $44.83 3. $132.44: $264.84/2 Page 4 1. 2 ½ miles: 10 laps x .25 2. 1,46 miles: 365 x 4 3. 34.6 degrees Farenheit: -128.6 + -94 Page 5 1. 6,766 minutes old: 4 x 24 = 96 hrs. + 16 hrs. =

112 hrs. x 60 = 6,720 min. + 46 min. 2. 15 mph: 3 hrs. x 60 = 180 min. + 36 min. =

217 minutes; 54 miles/216 = .25 mpmin.; .25 mpm x 60 min = 15mph

3. 61 feet: 47 + 14 Page 6 1. 170 miles: 34 miles round trip x 5 2. 40.6 miles: 5.8 x 7 3. 30 miles: 2 x 15 Page 7 1. $555.00 interest: $15,000.00 x .037 2. $47.03: $43.85 x .0725 = $3.18; $43.85 -

$3.18 3. $35.94: $5.99 x 6 Page 8 1. $17.41 total: $3.59 + $4.96 + $6.36 + $2.50 2. $9.20 savings: $73.99 - $64.79 3. $119.34 spent: $4.59 x 26 Page 9 1. 12 bags: 384/32 2. 2,472 pounds: 12 x 206 3. 28 truckloads: 75,600/2,700

Page 10 1. 146,421 stitches: 87 x 1,683 2. 1,947 more: 6,042 – 4,095 3. deli: sandwich @ the deli is $3.99, and $4.25

@ the convenient store Page 11 1. 10 hours: 3 + 3.5 + 3.5 hours 2. 8 hours: 7 + 10 + 7 + 8 hours = 32/4 3. 1 ½ hours: 42/28 Page 12 1. 92%: 96 + 88 + 100 + 84 = 367/4 2. 83%: 75 + 84 + 90 = 249/3 3. $80.36: $75.47 + $4.89 Page 13 1. 283.5 miles: 4.5 hours x 63 mph 2. 462 mph: 2,772/6 3. 36 mph: 24/40 = .6, .6 x 60 Page 14 1. 48 hours: 12 x 4 2. 42 minutes: 30 + 15 + 45 + 95 + 25 minutes =

210/5 3. 46 pages: 920/20 Page 15 1. 4.8 hours: .15 x 24 = 3.6 hours; .05 x 24 = 1.2

hours; 3.6 + 1.2 2. 7 ½ hours: 90 minutes x 5 = 450 minutes/60

minutes 3. 5 hours: 295 miles/59 mph Page 16 1. 84%: 86 + 97 + 69 + 83 + 91 + 78 = 504/6 2. 66 mph: 58 + 79 + 65 + 87 + 55 + 60 + 58 =

462/7 3. 66.5 degrees Fahrenheit: 85 + 56 + 65 + 60 =

266/4 Page 17 1. 42.5 hours: 8.5 hours x 5 2. 7.2 hours: .30 x 24 3. $48.31: $39.76 + $62.38 + $42.79 = $144.92 Page 18 1. 2.4 hours: .10 x 24 2. $166.24: $200.00 + $132.48 = $332.48/2 3. $2,764.00: $11,056.00/4

© 2003 Teachnology, Inc. 32

Page 19 1. 60%: 219/365 2. 55%: 726/1,320 3. 45%: 1,320 – 726 = 778/1,537 Page 20 1. 90%: 3,395 – 372 = 3,056.4; 3023/3,395 2. 10%: 100% - 15% - 75% = 3. 8.1 minutes or 8 minutes and 6 seconds: .18 x 45 Page 21 1. 45%: 10 hours x 60 minutes per hour + 48

minutes = 648/1440 minutes per day 2. 42,623.25 highway miles: .75 x 56,831 3. 22.5 hours: 30/2 = 15 x 1.5 Page 22 1. 99 inches: 2.75 x 36 2. 7 cm: .5 x 14 3. 3,073 inches: 482 x 6 6/16 ths or 482 x 6.375 Page 23 1. 33 meat eaters: .75 x 44 2. 115 members: .2 x 575 3. 45 minutes: 2 hours x 60 minutes per hour +

30 minutes = 150 minutes, 150 x .3 Page 24 1. 60% complete: 3/5 = .60 x 100 2. 68% complete: 17/25 x 100 3. 27 stores: 54/2 Page 25 1. 495 mailboxes: .25 x 660 = 165; 660 – 165 2. 48 days away: .75 x 64 3. 937 busses: 2/10 = .2; .2 x 4685 Page 26 1. 46 students: .4 x 115 2. 84 sedans: 3/5ths or .6 x 140 3. 265 students: 1/5 or .2 x 1,325 Page 27 1. 171 flights: 3/8 or .375 x 456 2. 25 students: 1/5 or .2 x 125 3. 3 hours: 8 – 5 Page 28 1. 16/24 or 2/3: 16 hours in a total of 24 hours 2. 1730: 17 days out of a total of 30 days in

September 3. 3/24 or 1/8: 3 hours in a total of 24

Page 29 1. 656 miles: 164 x 4 2. 75 hours: 2.5 x 30 (1/2 of 60) 3. 153 miles shorter: 539 - 386 Page 30 1. 80 miles: 3.2 x 25 2. 750 people: 30 x 25 3. 7,800 minutes: 5 x 52 = 260; 260 x 30 minutes

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