Inverse proportion: y = k/x

The Maths Habit
Walkthrough to print

  1. The cost, C pounds, of cheese is directly proportional to its mass, m kg. 3 kg costs £22.50. Find the cost of 5 kg.

    £37.50

  2. The distance a cyclist rides, d km, is directly proportional to the time, t hours. She rides 27 km in 1.5 hours. How far does she ride in 4 hours?

    72 km

  3. The number of tiles, n, is directly proportional to the area, A m². 4 m² needs 100 tiles. What area do 350 tiles cover?

    14 m²

A prize of £120 is shared equally.
What happens to each share
as more people join?

Each share gets smaller

Twice as many people: each share is half the size

y ∝ 1x

y = kx

Inverse proportion

  1. StatementWrite it with ∝ and 1 over.
  2. Replace ∝ with = kSwap the ∝ for = k.
  3. SubstitutePut in the pair of values you are given.
  4. Find kMultiply to find k.
  5. FormulaWrite the formula with k in.
  6. Use itPut in the new value and work it out.
y ∝ 1x
y = kx
y value = kx value
k = y value × x value
y = kx
y = knew x
inversely: 1 over x
k as a number
finding x? x = k ÷ y
Walkthrough to print

y is inversely proportional to x. When x = 5, y = 8. Find y when x = 4.

1Statementy ∝1x
2Replace ∝ with ky =kx
3Substitute8=k5
4Find kk =8×5=40
5Formulay =40x
6Use it, x = 4y =404=10

y is inversely proportional to x. When x = 3, y = 12. Find y when x = 9.

1Statementy ∝1x
2Replace ∝ with ky =kx
3Substitute12=k3
4Find kk =12×3=36
5Formulay =36x
6Use it, x = 9y =369=4

y is inversely proportional to x. When x = 5, y = 8. Find y when x = 4.

1Statementy ∝1x
2Replace ∝ with ky =kx
3Substitute8=k5
4Find kk =8×5=40
5Formulay =40x
6Use it, x = 4y =404=10

y is inversely proportional to x. When x = 6, y = 4. Find y when x = 8.

1Statementy ∝1x
2Replace ∝ with ky =kx
3Substitute4=k6
4Find kk =4×6=24
5Formulay =24x
6Use it, x = 8y =248=3

y is inversely proportional to x. When x = 5, y = 8. Find y when x = 4.

1Statementy ∝1x
2Replace ∝ with ky =kx
3Substitute8=k5
4Find kk =8×5=40
5Formulay =40x
6Use it, x = 4y =404=10

y is inversely proportional to x. When x = 2, y = 15. Find y when x = 10.

1Statementy ∝1x
2Replace ∝ with ky =kx
3Substitute15=k2
4Find kk =15×2=30
5Formulay =30x
6Use it, x = 10y =3010=3

y is inversely proportional to x. When x = 5, y = 8. Find y when x = 4.

1Statementy ∝1x
2Replace ∝ with ky =kx
3Substitute8=k5
4Find kk =8×5=40
5Formulay =40x
6Use it, x = 4y =404=10

T is inversely proportional to n. When n = 4, T = 9. Find T when n = 3.

1StatementT ∝1n
2Replace ∝ with kT =kn
3Substitute9=k4
4Find kk =9×4=36
5FormulaT =36n
6Use it, n = 3T =363=12

y is inversely proportional to x. When x = 5, y = 8. Find y when x = 4.

1Statementy ∝1x
2Replace ∝ with ky =kx
3Substitute8=k5
4Find kk =8×5=40
5Formulay =40x
6Use it, x = 4y =404=10

y is inversely proportional to x. When x = 3, y = 20. Find x when y = 5.

1Statementy ∝1x
2Replace ∝ with ky =kx
3Substitute20=k3
4Find kk =20×3=60
5Formulay =60x
6Use it, y = 5x =605=12

Inverse proportion: y = k/x worksheet, page 1

Answer sheet

  1. The time to fill a tank is inversely proportional to the flow rate. At 12 litres per minute it takes 20 minutes. What flow rate, in litres per minute, fills it in 15 minutes?

    16

  2. y ∝ 1x and y = 9 when x = 4. Find the positive value of x that makes y equal to x.

    6

  1. y is inversely proportional to x. When x = 4, y = 15. Find y when x = 6.

    y = 10

  2. y is inversely proportional to x. When x = 2, y = 18. Find x when y = 8.

    x = 4.5

  3. The time to fill a tank is inversely proportional to the number of pipes. 4 pipes take 45 minutes. How many pipes fill it in 30 minutes?

    6 pipes
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