2019 AMC 12B Problem 1

Problem 1 of 25EasierAlgebra

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?

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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.

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