# Proportion problems. How to solve those recipe questions on your maths GCSE paper.

In these examples, you will be given the values of two related quantities and you will be asked to find the value of one of the quantities when the other quantity changes. These simple types of proportion problems are common to many math tests.

**Example **

If I need 2 eggs to make a cake weighing 500g, how many eggs will I need to make a cake weighing 2500g?

First write down what you know and what you need to find:

500g = 2 eggs

2500g = ? eggs

All you need to do now is work out how many times bigger 2500g is than 500g:

2500 ÷ 500 = 5 times bigger:

So you need to multiply the amount of eggs also by 5:

2 × 5 = 10 eggs

**Example 2**

On average I can drive 70 miles on 3 gallons of fuel, how many miles can I drive on 24 gallons of fuel?

Again, let’s summarise the question, and write down what you know and what you need to find:

3 gallons = 70 miles

24 gallons = ? miles

Again, work out how many times bigger 24 is than 3:

24 ÷ 3 = 8 times bigger.

So you need to multiply 70 miles by 8:

70 × 8 = 560 miles

So I can drive 560 miles on 24 gallons of fuel.

**Example 3**

A survey is conducted on what is your favourite colour. 8 people said green was their favourite and the angle on the pie-chart for green is 40⁰:

a) Work out how many people said blue was their favourite colour, if the angle on the pie-chart for blue is 100⁰.

b) Work out the total number of people who were asked about their favourite colour.

a) Again, let’s summarise the question, and write down what you know and what you need to find:

40⁰ = 8 people

100⁰ = ? people

Firstly, work out how many times bigger 100 is than 40:

100 ÷ 40 = 2.5 times bigger.

So you need to multiply 8 people by 2.5:

8 × 2.5 = 20 people

b) To work out how many people were surveyed, you need to work out the number of people for 360⁰ (since there are 360⁰ in a full circle). Therefore:

40⁰ = 8 people

360⁰ = ? people

This time work out how many times bigger 360⁰ is than 40⁰:

360 ÷ 40 = 9 times bigger.

So you need to multiply 8 people by 9:

8 × 9 = 72 people

So 72 people were in the survey.