2005 AMC 12B 第 3 题

先试着解答 2005 AMC 12B 第 3 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 2005 AMC 12B 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

3.

Brianna 用周末工作赚来的部分钱购买若干张同价 CD。她用自己钱的五分之一买了全部 CD 的三分之一。买完全部 CD 后,她还剩下自己钱的几分之几?
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?
15\dfrac{1}{5}
13\dfrac{1}{3}
25\dfrac{2}{5}
23\dfrac{2}{3}
45\dfrac{4}{5}
答案:C
知识点:分数比与比例
小提示:
买全部 CD 的费用是买其中三分之一的三倍。
Buying all the CDs costs three times as much as buying one third of them
大提示:
全部 CD 花费她钱的 3⋅153\cdot\dfrac15。
All the CDs cost 3⋅153\cdot\dfrac15 of her money
解答:
全部 CD 的费用是三分之一 CD 费用的三倍,即她的钱的 3⋅15=353\cdot\dfrac15 = \dfrac35。
她还剩下自己钱的 1−35=251 - \dfrac35 = \dfrac25。
所以正确答案是 C。
Buying all the CDs costs three times what one third of them cost, namely 3⋅15=353\cdot\dfrac15 = \dfrac35 of her money.
She has 1−35=251 - \dfrac35 = \dfrac25 of her money left.
Thus, the correct answer is C.
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