# Ratio problems. How to share £42 between 2 people in the ratio 5:2.

## Ratio Word Problem Video

If you are given an amount and you need share this amount by a ratio then you can apply the following 3 steps to solve the problem:

Step 1

**Add** up all of the parts in the ratio.

Step 2

**Divide** the amount by your answer from step 1. This will tell you the value of 1 part of the ratio.

Step 3

**Multiply** the ratio by your answer from step 2. This will give you the quantities that you need.

**Example 1**

Jack and Jill have £42 to share between them. They share the money in the ratio 5:2 (Jack to Jill). Work out the amount of money Jack and Jill receive.

Step 1

**Add** up all of the parts in the ratio.

5 + 2 = 7

Step 2

**Divide** the amount by your answer from step 1.

42 ÷ 7 = £6

So each part of the ratio is equal to £6

Step 3

**Multiply** the ratio by your answer from step 2.

Jacks amount 5 × 6 = £30

Jills amount 2 × 6 = £12

You can check these answers are correct by adding them up to see if they give the original amount of money.

£30 + £12 = £42.

**Example 2**

Amy and Beth have £63 to share between them. They share the money in the ratio 4:5 (Amy to Beth). How much more money does Beth receive than Amy?

Step 1

**Add** up all of the parts in the ratio.

4 + 5 = 9

Step 2

**Divide** the amount by your answer from step 1.

63 ÷ 9 = £7

So each part of the ratio is equal to £7

Step 3

**Multiply** the ratio by your answer from step 2.

Amy’s amount 4 × 7 = £28

Jills amount 5 × 7 = £35

Like example 1, you can check these answers are correct by adding them up to see if they give the original amount of money.

£28 + £35 = £63

Now the question asked to find out how much more money Beth received than Amy:

£35 - £28 = £7.

So Beth received an extra £7 than Amy.

Let’s look at one more example of sharing an amount by a ratio given in a different context.

**Example 3**

In a box there are 126 chocolates. The chocolates are mixed in the ratio 3:2:1 (milk:white:dark). Work out how many of each type of chocolate are in the box.

Step 1

**Add** up all of the parts in the ratio.

3 + 2 + 1 = 6

Step 2

**Divide** the amount by your answer from step 1.

126 ÷ 6 = 21

So each part of the ratio is equal to 21 chocolates.

Step 3

**Multiply** the ratio by your answer from step 2.

Milk chocolates 2 1× 3 = 63

White chocolates 21 × 2 = 42

Dark chocolates 21 × 1 = 21

You can check these answers are correct by adding them up to see if they give the original amount of chocolates in the box:

63 + 42 + 21 = 126 chocolates.

So to summarise sharing an amount by a ratio remember the 3 steps of add, divide and multiply!

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