Question

Andy, Ben and Claire share £54. Ben gets three times as much money as Andy. Claire gets twice as much money as Ben. How much money does Claire get?

Answer 1

`£32.40`

Explanation:

Represent the amounts as a ratio:

Since Andy receives the least, let his amount be 1

Ben's amount is 3 times Andy's, so this will be 3

Claire's amount is 2 times Ben's so this will be 6

So we have:

`1:3:6`

We have £54.

So divide 54 by the sum of the numbers in the ratio:

`54/(6 + 3+1)= 5.4`

So:

Ben's amount = `3xx5.4= £16.20`

Andy's amount = `1 xx 5.4= £5.40`

Claire's amount = `6 xx 5.4= £32.40`

Check:

`£32.40 + £5.40 + £16.20 = £54.00`

You can also solve this as an equation:

Let `x=`Andy's amount since this is the least.

Ben's amount `3 xx`Andy's`= 3x`

Claire's amount `2xx` Ben's`=6x`

`6x+3x+x = 54 => 10x=54=> x=5.4`

Claire's amount `= 6xx 5.4= 32.40`