Keeping the Meaning in Mathematics: The Craft of Word Problems

CONTENTS OF CURRICULUM UNIT 07.06.08

  1. Unit Guide
  1. Objective
  2. Strategies
  3. Classroom Activities
  4. Appendix A
  5. Annotated Bibliography

The Art of Solving Word Problems by Using Proportions

Jill Elizabeth Smith

Published September 2007

Tools for this Unit:

Appendix A

1a. For a read-a-thon, a seventh grade class read 243 books in 4.5 weeks. If they read the same number of books every week, how many books were read per week?

243 books / 4.5 weeks = x books / 1 week

1b. For a read-a-thon, a seventh grade class read 243 books total. If they averaged 54 books per week, how many weeks did it take them to read all of them?

243 books / x weeks = 54 books / 1 week

1c. For a read-a-thon, a seventh grade class read books. They read 54 books per week and they did it for 4.5 weeks. How many books did they read total?

243 books / 4.5 weeks = x books / 1 week

2a. David read 45 pages of a book in 50 minutes. How many pages should he be able to read in 80 minutes?

45 pages / 50 min = x pages / 80 min

2b. David reads 45 pages of a book. If he can read 72 pages in 80 minutes, how long did it take him to read the 45 pages of the book?

45 pages / x min = 72 pages / 80 min

2c. David reads a book for 50 minutes. If he can read 72 pages in 80 minutes, how many pages will he read in the 50 minutes?

x pages / 50 min = 72 pages / 80 min

3. Jim found out that after working for 9 months he had earned 6 days of vacation time. How many days will he have earned after working for two years?

9 months / 6 days = 24 months / x days —> x = 16

4. Mary baked a batch of 3 dozen cookies for 40 women at the women's club. Next month the women's club is expecting 60 women to attend the monthly meeting, how many cookies should Mary bake?

3 dozen / 40 women = x dozen / 60 women —> x = 45

5. Last week, Amy worked seven hours each day Monday through Thursday, and eight hours on Saturday. She earned a total of $333. If her hourly rate was constant find the amount of money that Amy earned for each hour of work?

36 hrs / $333 = 1hr / x dollars —> x= $9.25

6. Shop-A-Lot Market is advertising 3 pounds of bananas for $2.37. Food Farm is advertising 2 pounds of bananas for $1.70. Which supermarket is advertising the lower price per pound for bananas?

3 lbs / $ 2.37 = 1 lb / x dollars and 2 lbs / $ 1.70 = 1 lb / x dollars —> Food Farm is cheaper.

7. Mr. Scrub offers three ways to pay for carwashes: a book of six car wash coupons for $33.00, a special offer of two washes for $11.50, or one was for $5.95. Which option offers the least expensive unit price for one car wash?

6 coupons / $ 33.00 = 1 coupon / x dollars and 2 coupons / $ 11.50 = 1 coupon / x dollars and 1 coupon / $ 5.95 = 1 coupon / x dollars —>6 coupons

8. For a read-a-thon, a fifth grade class read 243 books in 4.5 weeks. At this rate, how many books were read per week?

243 books / 4.5 weeks = x books / 1 week —> x = 54

9. It is 600 miles from San Diego to Napa Valley. Duane drove up to Napa on Tuesday. He averaged 50 mph. What was his travel time?

60 miles / x hours = 50 miles / 1 hour —> x = 12

10. Jim found out that after working for 9 months he had earned 6 days of vacation time. How many days will he have earned after working for two years?

9 months / 6 days = 24 months / x days —> x = 16

11. If 4 grapefruits sell for 79 cents, how much will 6 grapefruits cost?

4 grapefruits / $ 0.79 = 6 grapefruits / x dollars —> x = 1.19

12. Kelly takes inventory of her closet and discovers that she has 8 shirts for every 5 pairs of jeans. If she has 40 shirts, how many pairs of jeans does she have?

8 shirts / 5 jeans = 40 shirts / x jeans —> x = 25

13. David read 40 pages of a book in 50 minutes. How many pages should he be able to read in 80 minutes?

40 pages / 50 min = x pages / 80 min —> x = 64

14. Mr. Green has a garden. Of the 40 seeds he planted, 35% were vegetable seeds. How many vegetable seeds were planted?

x / 40 = 35% / 100 —> x = 14

15. Shelley ordered a painting. She paid 30% of the total cost when she ordered it, and she will pay the remaining amount when it is delivered. If she has paid $15, how much more does she owe?

15 / x = 30% / 100 —> x = 50 —> 50 - 15 = 35

16. Glucose is a type of sugar. A glucose molecule is composed of 24 atoms. Hydrogen atoms make up 50% of the atoms in the molecule, carbon atoms make up 25% of the molecule, and oxygen atoms make up the other 25 %. How many atoms of hydrogen are in a molecule of glucose?

x / 24 = 50% / 100 —> x = 12

17. Kylie usually makes 85% of her shots in basketball. If she shoots 20 shots, how many will she likely make?

x / 20 = 85% / 100 —> x = 17

18. In a high school survey, it was found that 240 of 600 students walk to school. What percent of the students walk to school?

240 / 600 = x % / 100 —> x = 40

19. A statue casts a shadow that is 360m long. At the same time, a person who is 2 m tall casts a shadow that is 6 m long. How tall is the statue?

x / 360 m = 2 m / 6 m —> x = 120

20. Paul swims in a pool that is similar to an Olympic-sized pool. Paul's pool is 30m long by 8 m wide. The length of an Olympic-sized pool is 50 m. To the nearest meter, what is the width of an Olympic-sized pool?

8 m (width) / 30 m (length) = x m (width) / 50 m (length) —> x = 13.3

21. A blueprint for a house states that 2.5 inches equals 10 feet. If the length of a wall is 12 feet, how long is the wall in the blueprint?

2.5 in / 10 ft = x in / 12 ft —> x = 3

22. A collector's model truck is scaled so that 1 inch on the model equals 6 ¼ feet on the actual truck. If the model is 2.3 inch high, how high is the actual truck?

1 in / 6.25 ft = 2.3 in / x ft —> x = 14.38 ft

23. Truss bridges use triangles in their support beams. Mark plans to make a model of a truss bridge in the scale 1 inch=12 feet. If the height of the triangles on the actual bridge is 40 feet, what will the height be on the model?

1 in / 12 ft = x in / 40 ft —> x = 3.33

24. On a map, every 2 inches represents an actual distance of 100 miles. Find the actual distance between two towns if the map distance is 5 inches.

2 in / 100 mi = 5 in / x mi —> x = 250

25. Murphy and Abby are trying to determine the distance between two particular cities by using a map. The map key indicates that 4.5 cm is equivalent to 75 km. If the cities are 12.7 cm apart on the map, what is the actual distance between the cities?

4.5 cm / 75 km = 12.7 cm / x km —> x = 212

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