So, the table for Desmond s Time shows a proportional relationship. The ratio between the time and the number of laps is always 73.

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1 Explain your reasoning. 1. An adult elephant drinks about 225 liters of water each day. Is the number of days the water supply lasts proportional to the number of liters of water the elephant drinks? 3. Which situation represents a proportional relationship between the number of laps run by each student and their time? Make a table and compare the number of days that an elephant s water supply lasts to the number of liters of water. Sample answer: The time to water ratio for 1, 2, 3, and 4 days is, or, or, and or. Since these ratios are all equal to, the number of days the supply lasts is proportional to the amount of water the elephant drinks. 2. An elevator ascends or goes up at a rate of 750 feet per minute. Is the height to which the elevator ascends proportional to the number of minutes it takes to get there? Make a table and compare the height to the time. The time to number of laps ratio for Desmond is always 73. or 73, or 73, or 73 The time to number of laps ratio for Maria is not always the same. or 75, or 80, or about 96.7 So, the table for Desmond s Time shows a proportional relationship. The ratio between the time and the number of laps is always 73. Copy and Solve Use a table to help you solve. Then explain your reasoning. Show your work on a separate piece of paper. 4. Plant A is 18 inches tall after one week, 36 inches tall after two weeks, 56 inches tall after three weeks. Plant B is 18 inches tall after one week, 36 inches tall after two weeks, 54 inches tall after three weeks. Which situation represents a proportional relationship between the plants height and number of weeks? The height to time ratio for 1, 2, 3, and 4 minutes is or 750, or 750, or 750, and or 750. Since these ratios are all equal to 750 ft per minute, the height to which the elevator ascends is proportional to the number of minutes it takes to get there. The table for plant B shows a proportional relationship. The ratio between the height and the number of weeks is always 18. esolutions Manual - Powered by Cognero Page 1

2 5. Determine whether the measures for the figure shown are proportional. 6. Justify Conclusions MegaMart collects a sales tax equal to of the retail price of each purchase. The tax is sent this to the state government. a. Is the amount of tax collected proportional to the cost of an item before tax is added? Explain. a. the length of a side and the perimeter b. the length of a side and the area b. Is the amount of tax collected proportional to the cost of an item after tax has been added? Explain. a. yes; Sample answer: The side length to perimeter ratio for side lengths of 1, 2, 3 and 4 units is, or, or, or. Since these ratios are all equal to, the measure of the side length of a square is proportional to the square s perimeter. b. no; Sample answer: The side length to area ratio for side lengths of 1, 2, 3 and 4 units is or 1, or, or, or. Since these ratios are not all equal, the measure of the side length of a square is not proportional to the square s area. a. Make a table and compare the tax collected to the cost of an item before tax is added. The tax to retail price ratios for 16, 32, 48, and 64 dollars are,,, and. Since these ratios are all equal, the amount of tax is proportional to the retail price of the item. b. Make a table and compare the amount of tax collected to the cost of an item after tax has been added. The tax to cost including tax ratios for 1, 2, 3, and 4 dollars of tax are,,, and. Since these ratios are all equal, the amount of tax is proportional to the cost of an item after tax has been added. esolutions Manual - Powered by Cognero Page 2

3 7. FIND THE ERROR Blake ran laps around the gym. His times are shown in the table. Blake is trying to decide whether the number of laps is proportional to the time. Find his mistake and correct it. Use the table and compare the number of laps to the time. The laps to time ratio for 4, 6, 8, and 10 laps is or 4, or 3, or 2, and or 2. Since these ratios are not all equal, the number of laps is not proportional to the time. 8. Persevere with Problems Determine whether the cost for ordering multiple items that will be delivered is sometimes, always, or never proportional. Explain your reasoning. The cost for delivered items will be proportional if all of the items cost the same amount. In addition, if a delivery fee is charged, the fee would have to be proportional to the number of items ordered. Sample answer: It depends on whether the items cost the same amount and if a delivery fee is charged; sometimes 9. Which relationship has a unit rate of 60 miles per hour? A. 300 miles in 6 hours B. 300 miles in 5 hours C. 240 miles in 6 hours D. 240 miles in 5 hours Find the unit rate in each relationship. A 300 miles 6 hours = 50 mi per hr B 300 miles 5 hours = 60 mi per hr C 240 miles 6 hours = 40 mi per hr D 240 miles 5 hours = 48 mi per hr The unit rate of 300 miles in 5 hours is 60 mi/hr. The answer is B. Explain your reasoning. 10. A vine grows 7.5 feet every 5 days. Is the length of the vine on the last day proportional to the number of days of growth? Make a table and compare the number of days to the length. or 1.5, or 1.5, or 1.5, or 1.5 It is proportional because the length to time ratios are all equal to 1.5 ft per day. esolutions Manual - Powered by Cognero Page 3

4 11. To convert a temperature in degrees Celsius to degrees Fahrenheit, multiply the Celsius temperature by and then add 32. Is a temperature in degrees Celsius proportional to its equivalent temperature in degrees Fahrenheit? Make a table and compare degrees Celsius to degrees Fahrenheit. 12. On Saturday, Querida gave away 416 coupons for a free appetizer at a local restaurant. The next day, she gave away about 52 coupons an hour. a. Is the number of coupons Querida gave away on Sunday proportional to the number of hours she worked that day? b. Is the total number of coupons Querida gave away on Saturday and Sunday proportional to the number of hours she worked on Sunday? a. Make a table and compare the number of coupons given away to the number of hours worked. Sample answer: The degrees Celsius to degrees Fahrenheit ratios for 0 C, 10 C, 20 C, and 30 C are or 0, or, or, and or. Since these ratios are not all equal, a temperature in degrees Celsius is not proportional to its equivalent temperature in degrees Fahrenheit. The coupons to hours ratios for 1, 2, 3, and 4 hours of work on Sunday are or 52, or 52, or 52, and or 52. Since these ratios are all equal to 52 coupons per hour, the number of coupons given away is proportional to the number of hours worked on Sunday. b. Make a table and compare the total number of coupons given away during the weekend to the number of hours worked on Sunday. Sample answer: The coupons to hours ratios for 1, 2, 3, and 4 hours of work on Sunday are or 468, or 260, or about 190, and or 156. Since these ratios are not all equal, the total number of coupons given away is not proportional to the number of hours worked on Sunday. esolutions Manual - Powered by Cognero Page 4

5 13. Justify Conclusions The fee for ride tickets at a carnival is shown in the table. 14. Mr. Martinez is comparing the price of oranges from several different markets. Which market s pricing guide is based on a constant unit price? a. Is the fee for ride tickets proportional to the number of tickets? Explain your reasoning. b. Can you determine the fee for 30 ride tickets? a. Use the table and compare the cost to mail a letter to its weight. The fee to ride tickets ratio for 5, 10, 15, 20, and 25 tickets is or 1, or about 0.95, or 0.90, and or Since these ratios are not all equal, the fee for is not proportional to the number of ride tickets. b. No; Sample answer: The fee increase is inconsistent. The table shows an increase of $4.50 from 5 to 10 tickets, an increase of $4 from 10 to 15 tickets, and an increase of $2.50 from 15 to 20 tickets. A. B. C. D. Find the unit price of oranges at each market. A $ = $0.70 per orange $ = $0.60 per orange The unit price is not constant. B $ = $0.70 per orange $ = $0.65 per orange The unit price is not constant. C $ = $0.60 per orange $ = $0.50 per orange The unit price is not constant. D $ = $0.60 per orange $ = $0.60 per orange $ = $0.60 per orange $ = $0.60 per orange The unit price is constant. The answer is D. esolutions Manual - Powered by Cognero Page 5

6 15. Short Response The middle school is planning a family movie night where popcorn will be served. The constant relationship between the number of people n and the number of cups of popcorn p is shown in the table. How many people can be served with 519 cups of popcorn? 19. 3x 2x 3(12) 2(12) = = 12 Use the table to find the constant relationship between n to p. The n to p ratio for 90, 180, and 360 people is 3, or 3, and or 3. The constant or 20. x = 0 = 3 relationship, or unit rate, is 3 cups of popcorn per person. Divide 519 by the unit rate to find the number of people that can be served with 519 cups of popcorn. Make a table to solve the situation. 22. Brianna downloads 9 songs each month onto her MP3 player. Show the total number of songs downloaded after 1, 2, 3, and 4 months. So, 173 people can be served with 519 cups of popcorn. Find the value of each expression if x = x 3(12) = x 4 2(12) 4 = 24 4 = x (12) + 30 = = 90 esolutions Manual - Powered by Cognero Page 6