AMC10 2019 B

AMC10 2019 B · Q1

AMC10 2019 B · Q1. It mainly tests Fractions.

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?

Alicia 有两个容器。第一个容器装满了 $\frac{5}{6}$ 的水，第二个容器是空的。她把第一个容器里的所有水倒入第二个容器，此时第二个容器装满了 $\frac{3}{4}$ 的水。较小容器的容积与较大容器的容积之比是多少？

(A) $\frac{5}{8}$ $\frac{5}{8}$

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

(D) $\frac{9}{10}$ $\frac{9}{10}$

(E) $\frac{11}{12}$ $\frac{11}{12}$

Answer

Correct choice: (D)

正确答案：（D）

Solution

Let $x$ be the volume of the first container and $y$ the volume of the second container. Then $\frac{5}{6}x = \frac{3}{4}y$, so $\frac{x}{y} = \frac{3}{4} \cdot \frac{6}{5} = \frac{9}{10}$.

设第一个容器的容积为 $x$，第二个容器的容积为 $y$。则 $\frac{5}{6}x = \frac{3}{4}y$，所以 $\frac{x}{y} = \frac{3}{4} \cdot \frac{6}{5} = \frac{9}{10}$。

Topics

AR.001 Fractions