Dependent and Independent Variables Worksheet Answer Key – Grade 6

Problem 1 Naming the variables

1. Independent: number of tickets sold. Dependent: money collected, because the money depends on how many tickets were sold.
2. Independent: minutes on the treadmill. Dependent: calories burned.
3. Independent: outside temperature. Dependent: number of lemonades sold.

(a) tickets → money; (b) minutes → calories; (c) temperature → lemonades

Problem 2 Who depends on whom?

The height depends on how many weeks have passed. Time moves on by itself, and the plant grows in response.

Dependent variable: h (height); independent variable: w

Problem 3 An equation from a price

The cost is $4 times the number of hours, so c = 4h. The cost depends on the hours.

c = 4h; the dependent variable is c

Problem 4 Complete the table

7 × 2 = 14, 7 × 4 = 28, 7 × 6 = 42, 7 × 8 = 56.

14, 28, 42, 56

Problem 5 Substitute the input

55 × 3 = 165. 55 × 6 = 330. 55 × 10 = 550.

d = 165, 330 and 550 miles

Problem 6 Equation from a table

18 ÷ 2 = 9, 27 ÷ 3 = 9, 45 ÷ 5 = 9, 72 ÷ 8 = 9. Each y is 9 times x.

y = 9x

Problem 7 Reading the ticket graph

Each ticket adds $5: (1, 5), (2, 10), (3, 15), (4, 20). So c = 5n. For 9 tickets: 5 × 9 = 45.

(a) c = 5n; (b) $45

Problem 8 An age difference

Zoe’s age is Leo’s age plus 4. For l = 9: z = 9 + 4 = 13. For z = 21: 21 = l + 4, so l = 21 − 4 = 17.

(a) z = l + 4; (b) 13 years old; (c) 17 years old

Problem 9 Muffin boxes

6 × 3 = 18, 6 × 5 = 30, 6 × 8 = 48, 6 × 12 = 72.

m = 6b

Problem 10 Graph from a table

Plot (2, 3), (4, 6) and (6, 9). Each y is 1.5 times x: 3 ÷ 2 = 1.5, 6 ÷ 4 = 1.5, 9 ÷ 6 = 1.5.

y = 1.5x

Problem 11 Song downloads

1.25 × 2 = 2.50, 1.25 × 4 = 5.00, 1.25 × 8 = 10.00, 1.25 × 10 = 12.50.

c = 1.25n

Problem 12 Which equation fits?

Each y is 5 more than x: 2 + 5 = 7, 4 + 5 = 9, 6 + 5 = 11, 8 + 5 = 13. The equation 5x would give 10 for x = 2, so it fails.

y = x + 5

Problem 13 The cyclist graph

1. After 3 hours the cyclist has traveled 36 miles.
2. Each hour adds 12 miles, so d = 12t. Check: 12 × 3 = 36.
3. 12 × 7 = 84.

(a) 36 miles in 3 hours; (b) d = 12t; (c) 84 miles

Problem 14 Cyclist versus runner

c = 14t and r = 9t.

1. At 3 hours: 14 × 3 = 42 and 9 × 3 = 27, and 42 − 27 = 15.
2. The gap is 14t − 9t = 5t. Set 5t = 25, so t = 5.

(a) 15 miles; (b) 5 hours

Problem 15 Hiking pace

1. d = 2.5t
2. 2.5 × 2 = 5, 2.5 × 4 = 10, 2.5 × 6 = 15.
3. 2.5 × 3.6 = 9.
4. 2.5t = 14, so t = 14 ÷ 2.5 = 5.6.

(a) d = 2.5t; (b) 5, 10, 15 miles; (c) 9 miles; (d) 5.6 hours

Problem 16 Food truck sales

1. The number of tacos n is independent. r = 3.75n.
2. 3.75 × 24 = 90.
3. 3.75n = 146.25, so n = 146.25 ÷ 3.75 = 39. Check: 3.75 × 39 = 146.25.

(a) r = 3.75n; (b) $90; (c) 39 tacos

Problem 17 Filling a kiddie pool

1. Time m is independent. The gallons depend on the minutes.
2. Each minute adds 18 gallons, so g = 18m.
3. 18 × 11 = 198.
4. 18m = 504, so m = 504 ÷ 18 = 28.

(a) minutes; (b) g = 18m; (c) 198 gallons; (d) 28 minutes

Problem 18 Weekend job pay

1. e = 11.5h
2. 11.5 × 6 = 69. 11.5 × 9 = 103.5. 11.5 × 13 = 149.5.
3. 11.5h = 230, so h = 20. Check: 11.5 × 20 = 230.

(a) e = 11.5h; (b) $69, $103.50, $149.50; (c) 20 hours

Problem 19 Two drones

1. Drone A gains 5 feet per second: a = 5t. Drone B gains 8 feet per second: b = 8t.
2. At 4 seconds: 32 − 20 = 12.
3. The gap is 8t − 5t = 3t. Set 3t = 27, so t = 9.

(a) a = 5t, b = 8t; (b) 12 feet; (c) 9 seconds

Problem 20 Trail mix comparison

1. Mix A: A = 6.40w. Mix B: B = 5.20w.
2. 6.40 × 7.5 = 48. 5.20 × 7.5 = 39. 48 − 39 = 9.
3. D = 6.40w − 5.20w = 1.20w. For w = 7.5: 1.20 × 7.5 = 9, which matches part (b).

(a) A = 6.40w, B = 5.20w; (b) $9; (c) D = 1.20w, $9