Question

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?

$\dfrac{5}{8}$

$\dfrac{4}{5}$

$\dfrac{7}{8}$

$\dfrac{9}{10}$

$\dfrac{11}{12}$

Solution:

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 Problem 1

Solution:

Problem 1 in Other Years