Combining Ratios

What is a Combining Ratio question?

A combining ratio question is when you are given two ratios that have a common variable and are asked to combine them into one overall ratio.

For instance, you know the ratios a:b and b:c and you are then asked to find the ratio a:b:c.

The way to solve these is to find a common multiple of the part that appears in both ratios.

In the example shown, a appears in both ratios so we find the lowest common multiple of 3 and 4 (which is 12). We multiply all parts of the ratio a:b by 4 and all parts of the ratio a:c by 3.

This gives the overall ratio a:b:c

Given that a:b = 3:7 and a:c = 4:3 Find the ratio a:b:c Give your answer in its simplest form.

Combining Ratio Question (Edexcel Higher, Specimen Set 2, Paper 2, Question 6)

Example Question

On a farm 

the number of cows and the number of sheep are in the ratio 6 : 5 

the number of sheep and the number of pigs are in the ratio 2 : 1 

The total number of cows, sheep and pigs on the farm is 189 

How many sheep are there on the farm?

On a farm the number of cows and the number of sheep are in the ratio 6 : 5 the number of sheep and the number of pigs are in the ratio 2 : 1 The total number of cows, sheep and pigs on the farm is 189 How many sheep are there on the farm?

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