Lesson 2.6 Skills Practice

Transcription

1 Lesson 2.6 Skills Practice Name Date Racing to the Finish Line! Using Direct Proportions Problem Set Complete each table. 1. The number of pipes a construction crew can install is directly proportional to the number of hours they work. Hours Worked Pipes Installed The number of meters Percy walks is directly proportional to the number of feet he walks. Meters Feet Chapter 2 Skills Practice 415

2 Lesson 2.6 Skills Practice page 2 3. The distance Ms. Juarez drives is directly proportional to the length of time she drives. Time (in hours) Distance (kilometers) The amount of water in a swimming pool is directly proportional to the length of time it has been filling up. Time (hours) Number of Gallons The cost of freshly-crushed peanut butter is directly proportional to the number of ounces of peanuts that are crushed. Peanuts (ounces) Cost of Peanut Butter (dollars) Chapter 2 Skills Practice

3 Lesson 2.6 Skills Practice page 3 Name Date 6. The cost of parking in a metered spot is directly proportional to the length of time parked. Time Parked (minutes) Cost to Park (dollars) Determine the constant of proportionality and tell what it represents in each situation. 7. The number of pages (p) Shirley reads is directly proportional to the time (t) she spends reading. Shirley reads 12 pages in 8 minutes. p 5 kt 12 5 k(8) k k k The constant of proportionality is 1, and it represents the number of pages Shirley reads 2 per minute. Chapter 2 Skills Practice 417

4 Lesson 2.6 Skills Practice page 4 8. The number of mini-muffins (m) Hector bakes is directly proportional to the number of cups (c) of mix that he uses. Hector uses 2.5 cups of mix to bake 45 mini-muffins. m 5 kc 45 5 k(2.5) k k k 5 18 The constant of proportionality is 18, and it represents the number of mini-muffins that can be made with each cup of mix. 9. The score (s) on a test is directly proportional to the number of questions (q) that the test taker answers correctly. Cindy scores 73.5 points by answering 21 questions correctly. s 5 kq k(21) k _ k k The constant of proportionality is 3.5, and it represents the number of points each question is worth. 418 Chapter 2 Skills Practice

5 Lesson 2.6 Skills Practice page 5 Name Date 10. The number of calories (c) in a bottle of juice is directly proportional to the number of servings (s) in the bottle. A bottle containing 6 servings of juice contains 390 calories. c 5 ks k(6) k k k 5 65 The constant of proportionality is 65, and it represents the number of calories per serving. 11. The distance (d ) a spring stretches is directly proportional to the weight (w) attached to the end of it. A spring stretches 8 centimeters when an object weighing 40 pounds is attached to it. d 5 kw 8 5 k(40) k k k The constant of proportionality is 0.2, and it represents the distance a spring stretches in centimeters for every pound of weight attached to it. Chapter 2 Skills Practice 419

6 Lesson 2.6 Skills Practice page The number of tokens (t) game players receive is directly proportional to the number of dollars (d) that they pay. Hailey pays $5 for 30 tokens. t 5 kd 30 5 k(5) k k k 5 6 The constant of proportionality is 6, and it represents the number of tokens game players receive for each dollar that they pay. 420 Chapter 2 Skills Practice

7 Lesson 2.6 Skills Practice page 7 Name Date Write and solve a direct variation equation to answer each question. 13. The number of words Lynne types is directly proportional to the number of minutes she types. Lynne types 320 words in 5 minutes. How long would it take her to type a document with 544 words? Let w represent the number of words and m represent the number of minutes. First calculate k. w 5 km k(5) k k k 5 64 Then, write and solve the equation with k w 5 64m m m m It would take her 8.5 minutes to type 544 words. Chapter 2 Skills Practice 421

8 Lesson 2.6 Skills Practice page The relationship between Mexican pesos and American dollars is a direct proportional relationship. During Kevin s vacation, Kevin exchanged 20 American dollars for 250 Mexican pesos. How many pesos would he receive for 50 dollars? Let m represent the number of Mexican pesos and a represent the number of American dollars. First calculate k. m 5 ka k(20) k k k Then, write and solve the equation with k m a m (50) m Kevin would receive 625 pesos for 50 dollars. 422 Chapter 2 Skills Practice

9 Lesson 2.6 Skills Practice page 9 Name Date 15. The length of a segment on a blueprint is directly proportional to the corresponding length in a house. A segment that is centimeters on the blueprint corresponds to a beam that is 21 feet long in the house. If the length of a segment on the blueprint is centimeters, what is the corresponding length in the house? Let b represent the length on the blueprint and h represent the length in the house. First calculate k. b 5 kh k(21) k k k Then, write and solve the equation with k b h m m m 5 27 If the length on the blueprint is centimeters, then the length in the house is 27 feet. Chapter 2 Skills Practice 423

10 Lesson 2.6 Skills Practice page The cost of a car rental is directly proportional to the number of days the car is rented. Mr. Thompson paid $602 to rent a car for 2 weeks. How much would he pay to rent a car for 5 days? Let p represent the amount he paid and d represent the number of days. First calculate k. Because 1 week 5 7 days, use d p 5 kd k(14) k k k 5 43 Then, write and solve the equation with k p 5 43d p 5 43(5) p Mr. Thompson would pay $215 for 5 days. 424 Chapter 2 Skills Practice

11 Lesson 2.6 Skills Practice page 11 Name Date 17. The number of bags of grass seed needed for a lawn is directly proportional to the size of the lawn. Ms. Carpenter needed 7 bags to cover 2800 square feet. How many bags does Mr. Larson need to buy if his lawn measures 3900 square feet? Let b represent the number of bags and s represent the number of square feet. First calculate k. b 5 ks 7 5 k(2800) k _ k k Then, write and solve the equation with k b s b (3900) b Because he can only buy whole bags, Mr. Larson would need to buy 10 bags of grass seed. Chapter 2 Skills Practice 425

12 Lesson 2.6 Skills Practice page The weight of an object on Earth is directly proportional to the weight of the object on the Moon. An astronaut who weighs 180 pounds on Earth would weigh 30 pounds on the Moon. If an object weighs 7 pounds on the Moon, how much would it weigh on Earth? Let e represent the weight on Earth and m represent the weight on the Moon. First calculate k. e 5 km k(30) k k k 5 6 Then, write and solve the equation with k 5 6. e 5 6m e 5 6(7) e 5 42 An object that weighs 7 pounds on the Moon would weigh 42 pounds on Earth. 426 Chapter 2 Skills Practice