Coins - A Question From An Aqa Foundation Specimen Paper

Ranjit has six coins in his pocket.
If he picks five of the coins, the most he could pick is £4.60.
The least he could pick is £2.70
How much money does he have altogether?

AQA New Specification Papers, published June 2015

It is necessary to know which coins are available.
They are £2, £1, 50p, 20p, 10p, 5p, 2p and 1p.

In order to make £4.60 from 5 coins, you need 2 x £2 and 3 x 20p. Although other possibilities exist, they will not answer the question. This method uses trial and error - though not too much!

Now, we need to change one coin, to have a total of £2.70
We discard one of the £2 coins we are left with 1 x £2 and 3 x 20p, which adds up to £2.60

To increase this to £2.70, we need to add a 10p coin.

Therefore, in total, Ranjit has 2 x £2 and 3 x 20p and 1 x 10p = £4.70
No other possibilities work.