AMC8 2002

AMC8 2002 · Q25

AMC8 2002 · Q25. It mainly tests Linear equations, Fractions.

Loki, Moe, Nick and Ott are good friends. Ott had no money, but the others did. Moe gave Ott one-fifth of his money, Loki gave Ott one-fourth of his money and Nick gave Ott one-third of his money. Each gave Ott the same amount of money. What fractional part of the group's money does Ott now have?

Loki、Moe、Nick 和 Ott 是好朋友。Ott 没有钱，但其他人有。Moe 给了 Ott 他钱的一第五，Loki 给了 Ott 他钱的一第四，Nick 给了 Ott 他钱的三分之一。每人都给了 Ott 等量的钱。Ott 现在拥有团体总钱款的几分之几？

(A) $\frac{1}{10}$ $\frac{1}{10}$

(B) $\frac{1}{4}$ $\frac{1}{4}$

(D) $\frac{2}{5}$ $\frac{2}{5}$

(E) $\frac{1}{2}$ $\frac{1}{2}$

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) Only the fraction of each friend’s money is important, so we can assume any convenient amount is given to Ott. Suppose that each friend gave Ott \$1. If this is so, then Moe had \$5 originally and now has \$4, Loki had \$4 and now has \$3, and Nick had \$3, and now has \$2. The four friends now have \$4 + \$3 + \$2 + \$3 = \$12, so Ott has $\frac{3}{12}=\frac{1}{4}$ of the group’s money. This same reasoning applies to any amount of money.

（B）每个朋友的钱所占的比例才是关键，因此我们可以假设给 Ott 的金额是任意方便的数。假设每个朋友都给了 Ott \$1。这样的话，Moe 原来有 \$5，现在有 \$4；Loki 原来有 \$4，现在有 \$3；Nick 原来有 \$3，现在有 \$2。四个朋友现在共有 \$4 + \$3 + \$2 + \$3 = \$12，所以 Ott 拥有该小组资金的 $\frac{3}{12}=\frac{1}{4}$。同样的推理适用于任何金额。

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