Lesson 5.3 Solving Direct Proportion Problems Write a direct variation equation and find the indicated value. 1. a varies directly as b, and a 5 4 when b 5 24. a) Write an equation that relates a and b. b) Find a when b 5 63. c) Find b when a 5 7. 2. w varies directly as v, and w 5 32 when v 5 80. a) Write an equation that relates w and v. b) Find w when v 5 120. c) Find v when w 5 25. 3. y varies directly as x, and y 5 18 when x 5 1 2. a) Write an equation that relates y and x. b) Find x when y 5 252. c) Find y when x 5 1 3. 68 Chapter 5 Lesson 5.3
In each table, p is directly proportional to q. Complete the following tables. 4. p 20 40? 5. p 1 3? q 4? 16 q? 27 90 Solve. Show your work. 6. The cost of baseball caps, C dollars, is directly proportional to the number of baseball caps, n, purchased. Eric purchased 12 baseball caps for $96. a) Find the cost of a baseball cap. b) Write an equation that relates C and n. c) Find the value of C when n 5 20. 7. The amount of money donated at a charity fundraising event, A, is directly proportional to the number of people, n, at the event. 6 people at the event donated a total of $120. a) Find the amount donated by each person at the event. b) Write an equation that relates the amount of money donated, A, and the number of people at the event, n. c) How much money did 50 people at the event donate? Extra Practice Course 2A 69
8. Elizabeth can type 275 words in 5 minutes. The number of words she types, w, is directly proportional to the length of time she takes to type, t minutes. a) Find the constant of proportionality. b) Write an equation that relates w and t. c) How many minutes will it take her to type a 935-word document? 9. Johnny needs to determine the height of each tree on his tree farm. He knows that the height of the tree, h feet, is directly proportional to the length of its shadow, d feet. The length of a shadow cast by a 8-foot tall tree is 5 feet. a) Find the constant of proportionality. b) Write an equation that relates the height, h, of the tree and the length of its shadow, d. c) Use your equation to find the height of a tree that casts a shadow 12 feet long. Use a proportion to solve each question. Show your work. 10. 4 cans of grapefruit juice cost $3.36. Find the cost of one dozen cans of grapefruit juice. 11. It costs $78 to rent a set of skis for 3 days. Find the cost of renting the skis for a week. 70 Chapter 5 Lesson 5.3
12. Elliot rides his bike at an average speed of 14 miles per hour. How many miles will he ride in 2 1 2 hours? 13. To make fruit punch, Susannah mixes lemonade with orange juice in the ratio 5 : 9. She uses 40 ounces of lemonade. How many ounces of orange juice does she use? 14. A machine can print 80 T-shirts in 10 minutes. Find the number of T-shirts the machine can print in an hour. 15. Jack buys a pair of shoes for $52 and pays $2.60 sales tax. How much sales tax will his friend pay if his friend purchases a shirt for $28? 16. A company invests $50,000 in a savings account that pays 3% interest per year. a) Write a direct proportion equation that relates interest, I, and years, t. b) How much interest will the company earn in 2 years? Extra Practice Course 2A 71
17. Janet works at a computer supply store and earns 4.5% commission on her total sales. Last week, she earned $130.50 in commission. Calculate her total sales for last week. 18. In an experiment, Peter mixes vinegar with a salt solution in the ratio 3 : 7. How many ounces of vinegar are needed to mix with 35 ounces of salt solution? 19. A machine can pack 60 packets of pasta in 5 minutes. a) How long does it take the machine to pack 240 packets of pasta? b) How many packets of pasta can the machine pack in an hour? 20. The cost of a piece of vacant land in New York City, C dollars, is directly proportional to the area of the land, a square feet. If a 2,000-square foot vacant lot cost $129,920, find the cost for a 3,600-square foot vacant lot. 72 Chapter 5 Lesson 5.3