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2019 AMC 12B Problem 1

Problem 1 of 25EasierArithmetic

Alicia had two containers. The first was 56\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 34\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 56V1=34V2.\dfrac{5}{6}V_1=\dfrac{3}{4}V_2. Then V1V2=3456=34⋅65=910. \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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Tagged: ratio and proportion · fraction

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