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Teaching mathematics
Teaching mathematics

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Best buys

Having proportional reasoning helps to ensure you get the best deals when shopping, particularly when it comes to offers and multi-buys. Often deals are misleading and larger ‘value’ packs can work out to be more expensive. It is important to be able to compare prices properly in order to make smart choices.

Activity 9 Example problem: washing-up liquid

Timing: Allow 5 minutes

Two shops, Fast-Save and Super-Mart, sell the same brand of washing-up liquid in the same size bottles (Figure 15).

At which shop is the washing-up liquid the best value for money?

Described image
Figure 15 Best buys


You need to be able to compare the two prices, so you need to find the price at each shop for a common number of bottles.

One approach to this problem is to find a common multiple of 5 and 6. In this case, 30 is a sensible choice as it is the lowest common multiple of 5 and 6.

The price for 30 bottles at Fast-Save is £17.10 (6 multiplication £2.85).

The price for 30 bottles at Super-Mart is £19.50 (5 multiplication £3.90).

An alternative approach would be to find the unit price for 1 bottle of washing-up liquid at each shop. This would involve dividing the cost by 5 and 6, respectively.