Working with Proportion (Edexcel IGCSE Maths)

Spec point — 1.7C

Working with proportion

What is direct proportion?

• Direct proportion

  • As one quantity increases/decreases by a certain rate (factor)
  • The other quantity will increase/decrease by the same rate

• The ratio of the two quantities is constant

  • E.g. 2 boxes of cereal is 800 g of cornflakes
  • Doubling the number of boxes of cereal (4 boxes) will double the amount of cornflakes (1600 g)

How do I solve direct proportion questions?

• Read through wordy direct proportion questions carefully

  • Ensure that you understand the context of the question
  • Some questions may tell you the relationship between the two values as a ratio

• Identify the two quantities involved

  • E.g. Hours worked and pay

• Find the factor that you will be increasing/decreasing by

  • This may be given to you in the question, e.g. 'the amount is tripled'

    • The quantity is multiplied by three

  • Alternatively, find the factor by dividing the 'new' quantity by the 'old' quantity

• Multiply the other quantity by this factor to find the required quantity

  • E.g. If three times as many hours are worked, the pay will be three times more in total

• Give your final answer in context

  • Round and give units where appropriate

Exam Hint You may have to round an answer to a whole number, but think carefully about the context of the question.

Sometimes you need to round up to the next whole number even if it is not the nearest.

E.g. If you need 1.3 tins of paint, round the number of tins required up to 2 to ensure that you have enough paint

What is the unitary method?

• The unitary method means finding one of something(1 unit of something)

  • This can be a useful strategy

• For example, find the weight of 7 boxes, if 8 boxes weigh 60 kg

  • Find the weight of 1 box (1 unit) using division

    • 60 kg ÷ 8 boxes = 7.5 kg per box

  • Scale this unit up using multiplication

    • 7.5 kg per box × 7 boxes = 52.5 kg

Worked Example The bonus received by an employee is directly proportional to the profit made by the company they work for. Bonuses are paid at a rate of £250 per £3000 profit the company makes.

(i) Work out the bonus an employee receives if the company makes a profit of £18 000.

(ii) If the company makes less than £600 profit, no bonus is paid.

Find the lowest bonus an employee could receive.

Answer:

(i)

Identify the two quantities 'profit' and 'bonus'

Find the factor ('new' ÷ 'old') from the profit

$\frac{18000}{3000}=6$

Multiply the bonus by the factor

$250\times6=1500$

Answer in context with units

An employee should receive a bonus of £1500

(ii)

We are still working with profit and bonus

The lowest bonus will be when the company makes exactly £600 profit

Find the factor using 'new' ÷ 'old'

$\frac{600}{3000}=\frac{1}{5}$

Find the amount of bonus by multiplying by the factor

$250\times\frac{1}{5}=50$

Answer in context with units

Final answer: The lowest amount of bonus an employee could receive is £50