Question

Pat and Alex have a combined total of £63.

The ratio of Pat’s money to Alex’s money is 5 : 2

They each spend an equal amount on sweets.

The ratio of Pat’s money to Alex’s money is now 3 : 1
How much did Pat spend on sweets?

Answer 1

£4.50

Explanation:

ratio of Pat : Alex = 5 : 2 = 5x : 2x ( where x is a multiplier )

then

5x + 2x = 63

7x = 63 ( divide both sides by 7 )

x = £ 9

Pat has 5 × £9 = £45

Alex has 2 × £9 = £18

let the amount they spend on sweets be x , then ratio of money is 3 : 1

so 45 - x : 18 - x = 3 : 1

express the ratio in fractional form and equate proportionally

`(45-x)/(18-x)` =
`(3)/(1)` ( cross- multiply )

45 - x = 3(18 - x)

45 - x = 54 - 3x ( add 3x to both sides )

45 + 2x = 54 ( subtract 45 from both sides )

2x = 9 ( divide both sides by 2 )

x = 4.5

Pat spent £4.50 on sweets