Sharing in a Ratio (WJEC GCSE Maths & Numeracy (Double Award): Foundation): Revision Note

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

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

$\begin{array}{rcl}& & \begin{array}{ccc}5\mathrm{parts}& =& 60\mathrm{litres}\\ ÷5& & ÷5\\ 1\mathrm{part}& =& 12\mathrm{litres}\end{array}\end{array}$

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

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

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

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