Problem Three students Peter, James, and Emma celebrated a math exam. Peter bought 5 beer bottles for £3 each, suggesting they split the cost three ways. After they ran out of beer, James bought another 3 bottles. At the end of the evening, Emma gave Peter £7 and James £1, saying they were now even. While Peter happily accepted money, James felt short-changed. Who cheated on the exam?
Solution Initially, the way Emma splits money seems unfair to James. Peter's contribution to James' has a ratio of 5:3, while Peter's refund to James' is 7 to 1. But here is a trick. They can't claim a refund for the beer they drank. Subtracting equal amounts from their contributions will lead to a completely different relationship between the refunds. This is how Emma calculated each share. You can use it when going out with your friends.
The total amount spent is £3x8=£24
Each should have paid £24:3=£8
Peter contributed £3x5=£15, so his refund is £15-£8=£7
James contributed £3x3=£9, so his refund is £9-£8=£1
Emma contributed £7+£1=£8, like everyone else.
So, who cheated on the math exam? Let's not jump to a conclusion. Maybe James just needed a good night's sleep.
Comments