Solve Problems Involving Ratio

In this activity, we will use what we know about ratio to solve some tricky problems. 

Example

Bobs and Babs are sharing the cost of a birthday cake for their Mum in the ratio of 3:2

The cake is £15.50, but the shop will give them a 20% discount.

How much is Bobs paying?

Answer

The first thing we should know about ratio is that the order of the ratio must follow the sentence.

 Bobs:Babs

3:2

We next need to work out the cost of the cake.

It costs £15.50  but there is a 20% discount.

We can either find 20% (10% = £1.55, so 20% = £3.10) and subtract that: £15.50 - £3.10 = £12.40

Or we can do 15.50 x 0.80 (remember, 0.8 gives us 80% which is 100% - 20% = 80%)

£15.50 x 0.80 = £12.40

The cake will cost them £12.40

Bobs and Babs are paying £12.40 in the ratio 3:2

Next, we divide the ratios to get the cost of 1 part:

12.40 ÷ (3 + 2) = 12.40 ÷ 5

= £2.48 for 1 part

Bobs is paying 3 parts:

3 x £2.48 = £7.44

Bobs pays £7.44

That was a lot to work through - did it make sense?

Let's have a go at some questions now.