Proportional Tables

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Proportional Tables · Grade 7 · Worksheet 3

1. x | y 2 | 34 7 | 119 12 | 204 17 | ? 22 | 374 If the table shows a proportional relationship, find the missing value of y when x = 17. Answer: 289 Solution: Check if the relationship is proportional by calculating y/x for each known pair. For x = 2, y = 34: 34/2 = 17 For x = 7, y = 119: 119/7 = 17 For x = 12, y = 204: 204/12 = 17 For x = 22, y = 374: 374/22 = 17 Since y/x = 17 for all pairs, the constant of proportionality k = 17.
   Full step-by-step solution

   Step 1: Check if the relationship is proportional by calculating y/x for each known pair. For x = 2, y = 34: 34/2 = 17 For x = 7, y = 119: 119/7 = 17 For x = 12, y = 204: 204/12 = 17 For x = 22, y = 374: 374/22 = 17 Step 2: Since y/x = 17 for all pairs, the constant of proportionality k = 17. Step 3: The equation is y = 17x. Step 4: Substitute x = 17: y = 17 * 17 = 289. The answer is 289.

2. Charlotte is organizing a school field trip and needs to rent buses. The bus company charges a proportional rate based on the number of buses rented. The table below shows the cost for renting different numbers of buses. If Charlotte needs to rent 11 buses for the entire grade, what will be the total cost? | Number of Buses | Total Cost ($) | |-----------------|----------------| | 3 | 450 | | 5 | 750 | | 8 | 1200 | Answer: 1650 Solution: Check if the relationship is proportional by calculating the cost per bus for each row. For 3 buses: 450 / 3 = 150 dollars per bus For 5 buses: 750 / 5 = 150 dollars per bus For 8 buses: 1200 / 8 = 150 dollars per bus All ratios are equal (150 dollars per bus), confirming a proportional…
   Full step-by-step solution

   Step 1: Check if the relationship is proportional by calculating the cost per bus for each row. For 3 buses: 450 / 3 = 150 dollars per bus For 5 buses: 750 / 5 = 150 dollars per bus For 8 buses: 1200 / 8 = 150 dollars per bus All ratios are equal (150 dollars per bus), confirming a proportional relationship. Step 2: Use the constant rate to find the cost for 11 buses. Cost = 150 dollars per bus * 11 buses = 1650 dollars. The total cost for renting 11 buses will be $1650.

3. Aroha is a beekeeper who tracks the relationship between the number of beehives she has and the kilograms of honey produced each season. The table below shows the honey production from her beehives. If the relationship is proportional, how many kilograms of honey will Aroha produce from 27 beehives? | Number of Beehives | Honey Produced (kg) | |--------------------|---------------------| | 3 | 21 | | 5 | 35 | | 9 | 63 | Answer: 189 Solution: Check if the relationship is proportional by finding the ratio of honey to beehives for each pair. For 3 beehives: 21 / 3 = 7 kg per beehive. For 5 beehives: 35 / 5 = 7 kg per beehive.
   Full step-by-step solution

   Step 1: Check if the relationship is proportional by finding the ratio of honey to beehives for each pair. For 3 beehives: 21 / 3 = 7 kg per beehive. For 5 beehives: 35 / 5 = 7 kg per beehive. For 9 beehives: 63 / 9 = 7 kg per beehive. The constant ratio is 7 kg per beehive, so the relationship is proportional. Step 2: Use the constant ratio to find honey for 27 beehives. Honey = 7 * 27 = 189 kg. The answer is 189.

4. x | y 2 | 28 4 | 56 6 | 84 8 | 112 10 | ? Complete the table for the proportional relationship. Find y when x = 10. Answer: 140 Solution: For x = 2, y = 28: y/x = 28/2 = 14 For x = 4, y = 56: y/x = 56/4 = 14 For x = 6, y = 84: y/x = 84/6 = 14 For x = 8, y = 112: y/x = 112/8 = 14 The constant of proportionality k = 14. The equation is y = 14x.
   Full step-by-step solution

   Step 1: Check that the relationship is proportional by verifying y/x is constant for the given rows. For x = 2, y = 28: y/x = 28/2 = 14 For x = 4, y = 56: y/x = 56/4 = 14 For x = 6, y = 84: y/x = 84/6 = 14 For x = 8, y = 112: y/x = 112/8 = 14 The constant of proportionality k = 14. Step 2: The equation is y = 14x. Step 3: Substitute x = 10 into the equation: y = 14 * 10 = 140. The answer is 140.

5. A proportional relationship is shown in a table where x represents the number of hours worked and y represents the earnings in dollars. The table has these values: (2, 36), (5, 90), (7, 126). If the relationship continues proportionally, what would be the earnings for working 11 hours? Answer: 198 Solution: Find the constant of proportionality (k) using any pair of values from the table. Using (2, 36): k = y/x = 36/2 = 18 Using (5, 90): k = y/x = 90/5 = 18 Using (7, 126): k = y/x = 126/7 = 18 All pairs give the same constant of proportionality: k = 18 Use the proportional relationship y = kx to…
   Full step-by-step solution

   Step 1: Find the constant of proportionality (k) using any pair of values from the table. Using (2, 36): k = y/x = 36/2 = 18 Using (5, 90): k = y/x = 90/5 = 18 Using (7, 126): k = y/x = 126/7 = 18 All pairs give the same constant of proportionality: k = 18 Step 2: Use the proportional relationship y = kx to find earnings for 11 hours. y = 18 × 11 Step 3: Calculate the result. y = 198 The earnings for working 11 hours would be $198.

6. A factory produces computer chips at a constant rate. The production table shows that in 3 hours they make 2,400 chips, and in 5 hours they make 4,000 chips. If the factory operates for 8 hours, how many chips will they produce? Answer: 6400 Solution: Step 1: Find the production rate per hour using the first data point: 2,400 chips ÷ 3 hours = 800 chips per hour Step 2: Verify with the second data point: 4,000 chips ÷ 5 hours = 800 chips per hour Step 3: Both calculations confirm the rate is 800 chips per hour Step 4: Calculate production for…
   Full step-by-step solution

   Step 1: Find the production rate per hour using the first data point: 2,400 chips ÷ 3 hours = 800 chips per hour Step 2: Verify with the second data point: 4,000 chips ÷ 5 hours = 800 chips per hour Step 3: Both calculations confirm the rate is 800 chips per hour Step 4: Calculate production for 8 hours: 800 chips/hour × 8 hours = 6,400 chips Step 5: The factory will produce 6,400 chips in 8 hours

7. x | y 1 | 21 3 | 63 6 | 126 11 | 231 ? | 336 Answer: 16 Solution: Check if the relationship is proportional by finding y/x for each pair. For (1, 21): 21/1 = 21 For (3, 63): 63/3 = 21 For (6, 126): 126/6 = 21 For (11, 231): 231/11 = 21 The constant of proportionality k = 21.
   Full step-by-step solution

   Step 1: Check if the relationship is proportional by finding y/x for each pair. For (1, 21): 21/1 = 21 For (3, 63): 63/3 = 21 For (6, 126): 126/6 = 21 For (11, 231): 231/11 = 21 The constant of proportionality k = 21. Step 2: The equation is y = 21x. Step 3: Substitute y = 336 into the equation: 336 = 21x. Step 4: Solve for x: x = 336 / 21 = 16. The answer is 16.