Proportional Relationships Worksheet Answer Key – Grade 7

Problem 1 Testing a Ticket Table

17.50 ÷ 5 = 3.5, 28 ÷ 8 = 3.5, 42 ÷ 12 = 3.5.

All ratios are equal.

Answer: Yes, proportional; k = 3.5 dollars per ticket

Problem 2 Gym Fee Table

8 ÷ 1 = 8, 13 ÷ 2 = 6.5, 18 ÷ 3 = 6, 23 ÷ 4 = 5.75.

The ratios are different.

Answer: Not proportional

Problem 3 Cookies per Cup of Flour

18 ÷ 1.5 = 12, 36 ÷ 3 = 12, 54 ÷ 4.5 = 12.

Each cup of flour makes 12 cookies.

Answer: k = 12 cookies per cup of flour

Problem 4 Proportional Graph Check

The points lie on a line that passes through the origin.

12 ÷ 3 = 4 and 24 ÷ 6 = 4.

Answer: Yes, proportional; k = 4

Problem 5 Straight Line, but Not Proportional

The line crosses the y-axis at (0, 4), not at (0, 0).

Ratios: 7 ÷ 2 = 3.5 and 10 ÷ 4 = 2.5 are different.

Answer: No, Jin is not correct, because the line does not pass through (0, 0)

Problem 6 Meaning of Key Points

(0, 0): 0 hours worked earn $0.

(1, 11.25): 1 hour of work earns $11.25.

Answer: (0, 0) means no work, no pay; (1, 11.25) means the unit rate is $11.25 per hour

Problem 7 Which Situation Is Proportional

(a) 1 pizza: 15, 2 pizzas: 26. 15 ÷ 1 ≠ 26 ÷ 2, and 0 pizzas would still cost $4. Not proportional.

(b) Distance = 3.2 × hours, so the ratio is always 3.2, and 0 hours gives 0 miles. Proportional.

(c) Ages 10 and 13, then 20 and 23: 13 ÷ 10 ≠ 23 ÷ 20. Not proportional.

Answer: Only (b) is proportional

Problem 8 Fractions in a Table

3 ÷ 12 = 6, 9 ÷ 32 = 6, 15 ÷ 52 = 6.

Answer: Proportional; k = 6 tablespoons per batch

Problem 9 Sprinkler Table

14 ÷ 5 = 2.8, 22.4 ÷ 8 = 2.8, 42 ÷ 15 = 2.8, so k = 2.8.

10 × 2.8 = 28.

Answer: 28 gallons

Problem 10 Comparing Two Tables

A: 9 ÷ 2 = 4.5, 18 ÷ 4 = 4.5, 27 ÷ 6 = 4.5.

B: 9 ÷ 2 = 4.5, 17 ÷ 4 = 4.25, 25 ÷ 6 ≈ 4.17.

Answer: Table A is proportional (k = 4.5); Table B is not

Problem 11 Water in a Tank

(a) 6 ÷ 4 = 1.5 and 12 ÷ 8 = 1.5, so k = 1.5 gallons per minute.

(b) 10 × 1.5 = 15.

Answer: k = 1.5; 15 gallons

Problem 12 Printer Speed from a Graph

26 ÷ 8 = 3.25.

The point (1, 3.25) is on the line, so 1 minute prints 3.25 pages.

Answer: k = 3.25 pages per minute

Problem 13 Paint Mixing Ratio

White ÷ blue = 53.

9 × 53 = 15, and 12 × 53 = 20.

Answer: 15 and 20 cups; k = 53 cups of white per cup of blue

Problem 14 Points That Do Not Line Up

3 ÷ 1 = 3, 6 ÷ 2 = 3, 8 ÷ 3 ≈ 2.67.

The third ratio differs, and the points do not form one straight line.

Answer: Not proportional

Problem 15 Lunch Receipt

(a) 22 ÷ 4 = 5.5, 33 ÷ 6 = 5.5, 49.5 ÷ 9 = 5.5. Yes, k = 5.5.

(b) 14 × 5.5 = 77.

(c) 77 ÷ 5.5 = 14.

Answer: Yes; $77.00 for 14 sandwiches; 14 sandwiches for $77.00

Problem 16 Window Washer

(a) 45 ÷ 12 = 3.75 minutes per window.

(b) 20 × 3.75 = 75 minutes.

(c) Cleaning 0 windows takes 0 minutes.

Answer: 3.75 min per window; 75 minutes; (0, 0) means 0 windows take 0 minutes

Problem 17 Taxi Fare

(a) The fare for 0 miles is $3.50, not $0, so the point (0, 0) is missing. Also 5.75 ÷ 1 = 5.75 but 8 ÷ 2 = 4. Not proportional.

(b) The price per mile is 8.00 − 5.75 = 2.25. Without the fee, k = 2.25 and 4 × 2.25 = 9.00.

Answer: Not proportional; k = $2.25 per mile; $9.00 for 4 miles

Problem 18 Robot Arm Movement

(a) 13 ÷ 2 = 6.5, 32.5 ÷ 5 = 6.5, 58.5 ÷ 9 = 6.5, so k = 6.5 cm per second.

(b) 12 × 6.5 = 78.

(c) 91 ÷ 6.5 = 14.

Answer: Proportional; 78 cm; 14 seconds

Problem 19 Two Text Plans

(a) Plan A: cost = 0.12 × texts, so k = 0.12 and (0, 0) is on the graph. Plan B costs $5.00 even for 0 texts, so it is not proportional.

(b) 40 texts: A = 4.80, B = 5 + 2 = 7.00. 100 texts: A = 12.00, B = 5 + 5 = 10.00.

(c) 40 texts: A is cheaper by 7.00 − 4.80 = 2.20. 100 texts: B is cheaper by 12.00 − 10.00 = 2.00.

Answer: Plan A is proportional (k = 0.12); A is $2.20 cheaper at 40 texts; B is $2.00 cheaper at 100 texts

Problem 20 3D Printer Filament

(a) 34 ÷ 32 = 12, 2 ÷ 4 = 12, 154 ÷ 152 = 12. So k = 12 gram per minute.

(b) 25 × 12 = 12 12.

(c) 9 ÷ 12 = 18.

Answer: k = 12; 12 12 grams; 18 minutes