Three students and eight beer bottles

Puzzle. Three students, Peter, James, and Emma, went out to celebrate their exams. Peter bought five beer bottles, each costing £3, whereas James bought three. At the night's end, Emma handed Peter £7 and James £1, saying they were even. Peter happily accepted, but James felt he was shorted. Who cheated in the math exam?

Three students went out to celebrate their exams.

Solution. Peter and James contributed 5 to 3 but were refunded 7 to 1, which may seem unfair. However, they can't claim back for the beer they consumed, and subtracting an equal amount from their contributions changes the refund ratio. This is how Emma calculated repayments; you can use this method when out with friends.

· Total money spent is £3x8=£24·  

· Each should pay £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

 So, did James cheat in his math exam? Well, maybe he just needed a good night's sleep to clear his head.

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