Rewrite $\frac{a}{b} = \frac{3}{7}$ in terms of $a$

$a = \frac{3}{7} b$

This means $a$ is $\frac{3}{7}$ of the size of $b$
Write this as a ratio

$a : b \frac{3}{7} : 1$

Multiply both sides of the ratio by 7 so the ratio is in terms of whole numbers

$a : b 3 : 7$

Rewrite $\frac{b}{c} = \frac{4}{5}$ in terms of $b$

$b = \frac{4}{5} c$

This means $b$ is $\frac{4}{5}$ of the size of $c$
Write this as a ratio

$b : c \frac{4}{5} : 1$

Multiply both sides of the ratio by 5 so the ratio is in terms of whole numbers

$b : c 4 : 5$

Ratios comparing $a$ and $b$ , and $b$ and $c$ [1]

To link the two ratios $a : b$ and $b : c$ we can use $b$ as a link
The ratios need to have the same number of parts for $b$
$a : b = 3 : 7$ and $b : c = 4 : 5$
Multiply $a : b$ by 4, and multiply $b : c$ by 7 so that the number of parts for $b$ in both ratios is 28

$a : b 12 : 28$

and

$b : c 28 : 35$

Method to find a common number of parts between two ratios [1]

The ratios are now linked by the same number of parts for $b$ , so can be written together

$a : b : c = 12 : 28 : 35$ [1]

Ratio Problem Solving (Edexcel GCSE Maths: Foundation)

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