Percentages and ratio · Ages 13–14

Direct proportion worksheet

Part of: Rates, ratios & proportions

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Percentages and ratio · Ages 13–14

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Write each answer in the space. For word problems, show your working and write a sentence answer.

1.4 storybooks cost $156, so 13 of them cost $
Answer:
2.y is in direct proportion to x, and y = 40 when x = 10. In y = kx, k = ; when x = 5, y = .
Fill in each blank
Answer:
3.3 cakes take 150 g of flour. How many of the same cakes do 400 g of flour make?
Answer:
4.y is in direct proportion to x: when x = 7, y = 1; when x = 56, y = ; when x = , y = 10.
Fill in each blank
Answer:
5.12 cakes take 720 g of flour. How many of the same cakes do 660 g of flour make?
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6.y is in direct proportion to x: when x = 40, y = 25; when x = 64, y = ; when x = , y = 20.
Fill in each blank
Answer:
7.y is in direct proportion to x. As x goes from 12 up to 16, y goes up by 14. When x = 12, y =
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8.y is in direct proportion to x. As x goes from 25 up to 50, y goes up by 30. When x = 25, y =
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9.In which set of values is y in direct proportion to x?
- A. (x, y) = (1, 16), (2, 8), (4, 4)
- B. (x, y) = (1, 11), (2, 15), (4, 23)
- C. (x, y) = (1, 8), (2, 9), (4, 11)
- D. (x, y) = (1, 4), (2, 8), (4, 16)
Choose the right answer
Answer:
10.y is in direct proportion to x. When x = 2, y = 6, so when x = 12, y = 16.
True or false?
Answer:
11.y is in direct proportion to x. If x goes up 10%, what happens to y?
- A. It goes down 10011%
- B. It goes down 10%
- C. It stays the same
- D. It goes up 10%
Choose the right answer
Answer:
12.y is in direct proportion to x. If x goes up 60%, what happens to y?
- A. It goes down 60%
- B. It goes down 37.5%
- C. It stays the same
- D. It goes up 60%
Choose the right answer
Answer:

13.A machine makes 60 toys every 12 minutes. At that rate, how many does it make in 4 hours?
Working:
Answer:
14.2 storybooks cost $32. How much more do 10 of them cost than 2? Put the steps in order.
- A. 160 − 32 = 128
- B. 16 × 10 = 160
- C. 32 ÷ 2 = 16
Write the letters in the right order
Working:
Answer:
15.Which two quantities are in direct proportion?
- A. A square's side and its area
- B. A person's age and height
- C. Speed and time over the same distance
- D. For notebooks at $8 each, the number bought and the total price
Choose the right answer
Working:
Answer:
16.Pay is in direct proportion to hours worked. 6 hours earn $450, so 9 hours earn $480.
True or false?
Working:
Answer:
17.A spring stretches 4 cm with 400 g hung on it. The stretch is in direct proportion to the weight. How far does it stretch with 300 g?
Working:
Answer:
18.A car uses 15 L of petrol over 190 km, its fuel use in direct proportion to distance. The tank held 34 L. How much is left after 190 km?
Working:
Answer:

Show the answers and working

Direct proportion worksheet: Answers and working

1. 507
The unitary method: one costs 156 ÷ 4 = 39, and 13 cost 39 × 13 = 507. Or a proportion: x : 13 = 156 : 4.
2. 4, 20
k = y ÷ x = 40 ÷ 10 = 4; y = 4 × 5 = 20.
3. 8 cakes
Each cake takes 150 ÷ 3 = 50 g, and 400 ÷ 50 = 8 cakes.
4. 8, 70
k = 1 ÷ 7 = 17: y = 17 × 56 = 8, and x = 10 ÷ (17) = 70.
5. 11 cakes
Each cake takes 720 ÷ 12 = 60 g, and 660 ÷ 60 = 11 cakes.
6. 40, 32
k = 25 ÷ 40 = 58: y = 58 × 64 = 40, and x = 20 ÷ (58) = 32.
7. 42
The rise in y is in proportion to the rise in x too: k = 14 ÷ (16 − 12) = 72, so y = 72 × 12 = 42.
8. 30
The rise in y is in proportion to the rise in x too: k = 30 ÷ (50 − 25) = 65, so y = 65 × 25 = 30.

9. D. (x, y) = (1, 4), (2, 8), (4, 16)
Direct proportion needs the same y ÷ x for every pair: 4 ÷ 1 = 8 ÷ 2 = 16 ÷ 4 = 4.
10. False
Direct proportion multiplies by the same number; it doesn't add the same amount: k = 6 ÷ 2 = 3, so y = 3 × 12 = 36.
11. D. It goes up 10%
y = kx: x becomes 1 + 10% times as much, so y does too, 10% up.
12. D. It goes up 60%
y = kx: x becomes 1 + 60% times as much, so y does too, 60% up.

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

13. 1200 toys
Same units first: 4 hours = 4 × 60 minutes. 60 ÷ 12 = 5 toys a minute, 4 × 60 × 5 = 1200.
14. C → B → A
The unitary method: one book, then 10 books, then the difference.
15. D. For notebooks at $8 each, the number bought and the total price
Total = 8 × number: total ÷ number is always 8, so they are in direct proportion.
16. False
450 ÷ 6 = 75 dollars an hour, and 9 hours make 75 × 9 = 675 dollars.
17. 3 cm
4 : 400 = x : 300, so x = 4 × 300 ÷ 400 = 3 cm.
18. 19 L
190 km use 15 × 190 ÷ 190 = 15 L, leaving 34 − 15 = 19 L.

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