Question

Alicia 有两个容器。第一个容器的水占其容量的 $\frac{5}{6}$ ，第二个是空的。她把第一个容器中的水全部倒入第二个容器，此时水占第二个容器容量的 $\frac{3}{4}$ 。较小容器体积与较大容器体积的比是多少？

Alicia had two containers. The first was $\frac{5}{6}$ full of water and the second was empty. She poured all the water from the first container into the second container, at which point the second container was $\frac{3}{4}$ full of water. What is the ratio of the volume of the smaller container to the volume of the larger container?

$\dfrac{5}{8}$

$\dfrac{4}{5}$

$\dfrac{7}{8}$

$\dfrac{9}{10}$

$\dfrac{11}{12}$

答案：D

知识点：分数比与比例

难度评级：770

解答：

设第一个和第二个容器的体积分别为 $F$ 和 $S$ 。水量既等于 $\dfrac56F$ ，也等于 $\dfrac34S$ ，所以 $\dfrac56F=\dfrac34S$ 。

因此 $\dfrac{F}{S}=\dfrac{3/4}{5/6}=\dfrac9{10}$ 。第一个容器较小，所以所求体积比为 $\dfrac9{10}$ 。所以正确答案是 D。

Let the volumes of the first and second containers be $F$ and $S$ . The amount of water is both $\dfrac56F$ and $\dfrac34S$ , so $\dfrac56F=\dfrac34S$ .

Thus $\dfrac{F}{S}=\dfrac{3/4}{5/6}=\dfrac9{10}$ . Since the first container is smaller, the ratio of the smaller container to the larger container is $\dfrac9{10}$ . Thus, D is the correct answer.

2019 AMC 10B 第 1 题

答案：D

难度评级：770

解答：

其他年份的第 1 题