P6 / Raffles Girls / 2020 / SA2 Prelims / Paper 2 – Q17 [5 marks]

Question:

Peter, Roger and Mary each had a sum of money. They decided to split their dinner bill equally.
If Roger were to pay for the bill first, the sum of his remaining money would be 4/9 of Mary’s money.
If Mary were to pay for the bill first, the sum of her remaining money would be 11/15 of Roger’s money.
If Peter were to pay for the bill first, he would have used up all his money.
(a) Given that Mary had $126 more than Roger, how much was each person’s share of the bill?
(b) Express Peter’s sum of money as a fraction of their total sum of money.