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Fair payment for shared wheat among three

Question

Three housemates pool and share equally whatever they gather. One day Alice brings in 55 bushels of wheat, Bob brings 33, and Cory brings none. Cory pays $8 to compensate the other two for his share. If the money is divided fairly, how much more does Alice receive than Bob?

Short answer

$6. Each person consumes 83\tfrac83 bushels, so Alice supplies 5−83=735-\tfrac83=\tfrac73 to Cory and Bob only 13\tfrac13. Cory's $8 splits 7:17:1, so Alice gets $7 and Bob $1.

Adapted from QuantQuestions.io; question and answer rewritten by SelfMadeQuant.com.

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