2019 AMC 12B Problem 1

Question

Alicia had two containers. The first was

\dfrac{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

\dfrac{3}{4}

full of water. What is the ratio of the volume of the first container to the volume of the second container?

\dfrac{5}{8}

\dfrac{4}{5}

\dfrac{7}{8}

\dfrac{9}{10}

\dfrac{11}{12}

Answer: D

Concepts:ratio and proportion fraction

Difficulty rating: 880

Small hint:

The amount of water is unchanged when it is poured

Big hint:

\dfrac{5}{6}V_1=\dfrac{3}{4}V_2

Solution:

The volume of water is the same before and after, so

\dfrac{5}{6}V_1=\dfrac{3}{4}V_2.

Then

\dfrac{V_1}{V_2}=\dfrac{\frac{3}{4}}{\frac{5}{6}}=\dfrac{3}{4}\cdot\dfrac{6}{5}=\dfrac{9}{10}.

Thus, D is the correct answer.