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Finding unknown ratios

Using a diagram can help to answer ratio problems.

Example

The ratio of boys to girls in a team is \(3 : 4\). There are 8 girls. How many boys are there?

There are 8 girls shared into 4 parts. Each part has \(\frac{8}{4}= 2 \:\text{girls}\).

Fill in the diagram using this information.

A ratio diagram to help work out the ratio of boys to girls in the ratio of 3:4. Boy’s boxes are blank and the girl’s contain 4 sets of 2.

Now because the amounts are shared equally between all of the parts, the rest of the table can be filled in.

A completed ratio diagram to show the ratio of boys to girls in the ratio of 3:4. Boys boxes contain 3 sets of 2 and the girls contain 4 sets of 2.

From the diagram it is clear that the number of boys in the team is \(2 \times 3 = 6\).