2019 AMC 10B Problem 1

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}

Answer: D

Concepts:fraction ratio and proportion

Difficulty rating: 770

Small hint:

Let the container volumes be variables

Big hint:

Equate the same water amount before and after pouring

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{\frac{3}{4}}{\frac{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.