Direct proportion: worded problems

The Maths Habit

  1. y is directly proportional to x. When x = 4, y = 26. Find y when x = 10.

    y = 65

  2. y is directly proportional to x. When x = 15, y = 6. Find y when x = 40.

    y = 16

  3. P is directly proportional to Q. When Q = 3, P = 21. Find Q when P = 56.

    Q = 8

A car uses 6 litres of fuel
to go 80 km.
What else can you work out?

12 litres takes it 160 km

3 litres takes it 40 km

1 litre takes it about 13 km

Write a formula

Pay, P, is directly proportional
to hours, h P = kh

12 m of cable cost £54. How much does 1 m cost?

metres£00112544.50

÷ 12 on both lines: 54 ÷ 12 = £4.50

£4.50 for each metre is k, so C = 4.5L. How much do 20 m cost?

metres£0014.5012542090

C = 4.5 × 20 = £90

The cost of fuel, C pounds, is directly proportional to the volume, v litres. 30 litres costs £45. Find the cost of 42 litres.

Start with C ∝ v
C = kv, 45 = 30k, k = 1.5
C = 1.5v
C = 1.5 × 42 = £63

The length of a shadow, s metres, is directly proportional to the height, h metres. A 4 m post has a 10 m shadow. Find the shadow of a 7 m tree.

Start with s ∝ h
s = kh, 10 = 4k, k = 2.5
s = 2.5h
s = 2.5 × 7 = 17.5 m

The cost of fuel, C pounds, is directly proportional to the volume, v litres. 30 litres costs £45. Find the cost of 42 litres.

Start with C ∝ v
C = kv, 45 = 30k, k = 1.5
C = 1.5v
C = 1.5 × 42 = £63

Euros, E, are directly proportional to pounds, p. £80 buys 92 euros. How many euros does £130 buy?

Start with E ∝ p
E = kp, 92 = 80k, k = 1.15
E = 1.15p
E = 1.15 × 130 = 149.50 euros

The cost of fuel, C pounds, is directly proportional to the volume, v litres. 30 litres costs £45. Find the cost of 42 litres.

Start with C ∝ v
C = kv, 45 = 30k, k = 1.5
C = 1.5v
C = 1.5 × 42 = £63

The mass of a wire, m grams, is directly proportional to its length, L metres. 5 m of wire has a mass of 340 g. Find the mass of 8 m of wire.

Start with m ∝ L
m = kL, 340 = 5k, k = 68
m = 68L
m = 68 × 8 = 544 g

The cost of fuel, C pounds, is directly proportional to the volume, v litres. 30 litres costs £45. Find the cost of 42 litres.

Start with C ∝ v
C = kv, 45 = 30k, k = 1.5
C = 1.5v
C = 1.5 × 42 = £63

The mass of flour, f grams, is directly proportional to the number of biscuits, n. 24 biscuits need 300 g of flour. How many biscuits can be made with 450 g?

Start with f ∝ n
f = kn, 300 = 24k, k = 12.5
f = 12.5n
450 = 12.5n, n = 36 biscuits

The cost of fuel, C pounds, is directly proportional to the volume, v litres. 30 litres costs £45. Find the cost of 42 litres.

Start with C ∝ v
C = kv, 45 = 30k, k = 1.5
C = 1.5v
C = 1.5 × 42 = £63

The time to download a file, t seconds, is directly proportional to its size, s MB. A 40 MB file takes 16 seconds. How long does a 65 MB file take?

Start with t ∝ s
t = ks, 16 = 40k, k = 0.4
t = 0.4s
t = 0.4 × 65 = 26 seconds

Direct proportion: worded problems worksheet, page 1

Answer sheet

  1. A recipe uses 300 g of flour for every 120 g of butter. Sam has 500 g of flour and 180 g of butter. Which runs out first?

    The butter

  2. y is directly proportional to x. When x goes up by 5, y goes up by 12. Find y when x = 20.

    48

  3. The number of tiles, N, needed for a floor is directly proportional to its area, A m2. A floor of 18 m2 needs 450 tiles. What area can be covered with 700 tiles?

    28 m2

  1. The cost, C pounds, of rope is directly proportional to its length, L metres. 8 m costs £20. Find a formula for C in terms of L.

    C = 2.5L

  2. Pay is directly proportional to hours worked. 6 hours pays £75. Find the pay for 10 hours.

    £125

  3. Fuel used is directly proportional to distance.
    A car uses 3 litres for 40 km.
    How far does it go on 7.5 litres?

    100 km
Exit tickets to print