Sharing in a Ratio (Edexcel IGCSE Maths)

Spec point — 1.7B

Sharing in a ratio

How do I share an amount in a given ratio?

• Add together all parts in the ratio to find the total number of parts in the whole

  • £200 is to be shared between two people, A and B, in the ratio 5:3
  • There are 8 “parts” in total, as A receives 5 parts and B receives 3 parts

• Divide the amount being shared by the total number of parts

  • £200 must be split into 8 parts, so this means that 1 part must be worth £25

    • 200 ÷ 8 = 25

• Multiply the amount each part is worth by the number of parts for each quantity in the ratio

  • Person A receives 5 parts, each worth £25

    • 5 × 25 = £125 for person A

  • Person B receives 3 parts, each worth £25

    • 3 × 25 = £75 for person B

• Check the values in the new ratio add up to the total amount being shared

  • £125 + £75 = £200

Exam Hint Adding labels to your ratios will help make your working clearer and help you remember which number represents which quantity, e.g., $\begin{gathered} \mathrm{A} : \mathrm{B} \\ 3 : 4 \end{gathered}$

Worked Example A particular shade of pink paint is made using three parts red paint, to two parts white paint. Mark needs 60 litres of pink paint in order to decorate rooms in a school.

Calculate the volume of red and white paint that Mark needs to purchase in order to have enough paint to decorate the rooms.

Answer:

The ratio of red to white is

3 : 2

Adding these together gives the total number of parts

3 + 2 = 5

The total amount of paint is 60 litres

∴ 5 parts = 60 litres

Divide both sides by 5 to find out the number of litres in one part

$\begin{gathered} \begin{gathered} 5 \text{parts} & = 60 \text{litres} \\ \div 5 & \div 5 \\ 1 \text{part} & = 12 \text{litres} \end{gathered} \end{gathered}$

The ratio was 3:2, so multiply both number of parts by 12

$\begin{gathered} \mathrm{R} : \mathrm{W} \\ 3 : 2 \\ \begin{gathered} \times 12 & \downarrow \end{gathered} \begin{gathered} \downarrow \times 12 \end{gathered} \\ 36 : 24 \end{gathered}$

Answer in context, making sure you make it clear which value is associated with which colour paint

Final answer: Mark will need to buy 36 litres of red paint and 24 litres of white paint