Question

一个大袋子里装有一美分、十美分和二十五美分硬币。十美分硬币的数量是一美分硬币的两倍，二十五美分硬币的数量是十美分硬币的三倍。袋中可能装有的钱数是

A large bag of coins contains pennies, dimes and quarters. There are twice as many dimes as pennies and three times as many quarters as dimes. An amount of money which could be in the bag is

$\$306$

$\$333$

$\$342$

$\$348$

$\$360$

答案：C

知识点：整除性钱币比与比例

难度评级：1270

小提示：

设一美分硬币的数量为 $p$

Let the number of pennies be $p$

大提示：

用 $p$ 的倍数表示硬币总价值（单位：美分）

Express the total value in cents as a multiple of $p$

解答：

若有 $p$ 枚一美分硬币，则有 $2p$ 枚十美分硬币和 $6p$ 枚二十五美分硬币。总价值为 $p+10(2p)+25(6p)=171p$ 美分。所列美元数中， $34200=171\cdot200$ 美分是可能的。

所以正确答案是 C。

If there are $p$ pennies, there are $2p$ dimes and $6p$ quarters. Their total value is $p+10(2p)+25(6p)=171p$ cents. Of the listed dollar amounts, $34200=171\cdot200$ cents is possible.

Thus the correct answer is C.

1985 AMC 12 第 4 题

答案：C

难度评级：1270

小提示：

大提示：

解答：

其他年份的第 4 题