AMC12 2005 B

AMC12 2005 B · Q3

AMC12 2005 B · Q3. It mainly tests Fractions, Ratios & proportions.

Brianna is using part of the money she earned on her weekend job to buy several equally-priced CDs. She used one fifth of her money to buy one third of the CDs. What fraction of her money will she have left after she buys all the CDs?

布里安娜用她周末工作赚的一部分钱购买了若干张价格相同的CD。她用她钱的五分之一买了CD的三分之一。她买完所有CD后，还剩下她钱的几分之几？

(A) $\frac{1}{5}$ $\frac{1}{5}$

(B) $\frac{1}{3}$ $\frac{1}{3}$

(D) $\frac{2}{3}$ $\frac{2}{3}$

(E) $\frac{4}{5}$ $\frac{4}{5}$

Answer

Correct choice: (C)

正确答案：（C）

Solution

Let $m =$ Brianna's money. We have $\frac15 m = \frac13 (\mbox{CDs}) \Rightarrow \frac35 m = (\mbox{CDs})$. Thus, the money left over is $m-\frac35m = \frac25m$, so the answer is $\boxed{\textbf{(C) }\frac{2}{5}}$. This was just a simple manipulation of the equation. No solving was needed!

设 $m =$ 布里安娜的钱。我们有 $\frac15 m = \frac13 (\mbox{CDs}) \Rightarrow \frac35 m = (\mbox{CDs})$。因此，剩下的钱是 $m-\frac35m = \frac25m$，所以答案是 $\boxed{\textbf{(C) }\frac{2}{5}}$。这只是对等式的简单变形，不需要求解！

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