Question

D The prize money for a competition is

shared between the winner and the runner-up
in the ratio 3: 1.
The winner received £250 more than the
runner-up.
What was the total prize money?

Answer 1

Total amount = £500

Explanation:

Let the amount for the runner up be = x

Let the amount for winner be = x + 250

Let the total amount be x + x + 250 = 2x + 250

Ratio of the amount is 3 : 1

Sum of the ratio = 3 + 1 = 4

Amount for the winner is

`(3)/(4) \ of \ (2x + 250) = (x + 250)\\\\(3)/(4)*(2x + 250) = x + 250\\\\(6x)/(4) + (750)/(4) = x + 250\\\\(6x)/(4) - x = 250 - (750)/(4)\\\\(6x - 4x)/(4) = (1000 - 750)/(4)\\\\(2x)/(4) = (250)/(4) \\\\2x = 250\\\\x = 125`

Therefore, Amount won by runner - up = x = £125

Amount won by winner = x + 250 = 125 + 250 = £375

Therefore, total amount = 375 + 125 = £500

Answer 2

Answer: 333.3

Explanation: