Puzzle Three students, Peter, James, and Emma, passed their math exam and celebrated at the bar. Peter had a student discount. So he suggested he buy 5 beer bottles, costing £3 each, and they split the cost three ways. After a while, they ran out of beer and James, who also had a discount, bought another 3 bottles. At the end of the evening, Emma gave Peter £7 and James £1, saying they are now even. Peter happily accepted, but James felt short-changed. Which of them cheated on the exam?
Solution At first glance, the split does look unfair to James. The ratio of Peter's contribution to his is 5:3, while the ratio of refund is 7:1. But here is a trick. They can't claim a refund for the beer they drank. Subtracting an equal amount from their contributions will lead to a completely different compensation ratio.
If you had a similar situation when going out with friends, here is how to calculate your shares.
Total amount spent is £3x8=£24,
Each should pay £24:3=£8.
Peter contributed £3x5=£15, so his refund £15 - £8 = £7
James contributed £3x3=£9, so his' refund is £9 - £8 = £1
Emma gave £7 to Peter and £1 to James, making herself £8 out of pocket, like everyone else.
So, who cheated on the exam? Let's not be hasty. Maybe James just needed a good night's sleep))
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