2019 AMC 10B Problems/Problem 1

The following problem is from both the 2019 AMC 10B #1 and 2019 AMC 12B #1, so both problems redirect to this page.

Problem

Alicia had two containers. The first was $\tfrac{5}{6}$ 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 $\tfrac{3}{4}$ full of water. What is the ratio of the volume of the first container to the volume of the second container?

$\textbf{(A) } \frac{5}{8} \qquad \textbf{(B) } \frac{4}{5} \qquad \textbf{(C) } \frac{7}{8} \qquad \textbf{(D) } \frac{9}{10} \qquad \textbf{(E) } \frac{11}{12}$

Solution

Let the first jar's volume be $A$ and the second's be $B$ . It is given that $\frac{3}{4}A=\frac{5}{6}B$ . We find that $\frac{B}{A}=\frac{3/4}{5/6}=\boxed{\frac{9}{10}}.$

We already know that this is the ratio of smaller to larger volume because it is less than $1.$

--mguempel

2019 AMC 10B (Problems • Answer Key • Resources)
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All AMC 10 Problems and Solutions

2019 AMC 12B (Problems • Answer Key • Resources)
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All AMC 12 Problems and Solutions

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2019 AMC 10B Problems/Problem 1

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