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Equal Rations

专题
Brainteaser / 脑筋急转弯
难度
L2

题目详情

Josiah、Charles 和 Michael 一起住在小屋里，所有东西都平均分享。今天，Josiah 带回了 5 蒲式耳小麦，Charles 带回了 3 蒲式耳小麦，而 Michael 没带任何小麦。作为补偿，Michael 另外给出 $8，供 Josiah 和 Charles 分配。Josiah 比 Charles 多拿了多少钱？

Josiah, Charles, and Michael live together in a cottage and share everything equally. Today, Josiah has brought home five bushels of wheat, Charles has brought home three bushels of wheat, and Michael has brought home none. To compensate, Michael gives $8 instead for Josiah and Charles to share. How much more money did Josiah receive than Charles?

解析

因为三个人要平均分配所有东西，所以每个人都能分到 83\frac{8}{3} 蒲式耳小麦，其中也包括 Michael。这样一来，Josiah 实际上给了 Michael 5−83=735-\frac{8}{3} = \frac{7}{3} 蒲式耳，Charles 实际上给了 Michael 3−83=133-\frac{8}{3} = \frac{1}{3} 蒲式耳。Michael 一共拿到 83\frac{8}{3} 蒲式耳，并为此支付了 $8，因此每 13\frac{1}{3} 蒲式耳对应 $1。于是 Josiah 应得 $7，Charles 应得 $1，所以 Josiah 比 Charles 多拿 $6。

Original Explanation

Since the cottage folk split everything equally, everyone will get 83\frac{8}{3} bushels of wheat, including Michael. Of this, Josiah contributes 5−83=735-\frac{8}{3} = \frac{7}{3} and Charles contributes 3−83=133 - \frac{8}{3} = \frac{1}{3} to Michael. Because Michael receives 83\frac{8}{3} bushels of wheat in exchange for $8, each 13\frac{1}{3} bushels costs $1. If each 13\frac{1}{3} bushel costs $1, Josiah receives $7 and Charles receives $1. Therefore, Josiah receives $6 more than Charles.