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Water, water, everywhere...

Source: 2019 AMC 10B #1/12B #1

February 14, 2019

Problem Statement

Alicia had two containers. The first was 56\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 34\tfrac{3}{4} full of water. What is the ratio of the volume of the first container to the volume of the second container?
<spanclass=latexbold>(A)</span>58<spanclass=latexbold>(B)</span>45<spanclass=latexbold>(C)</span>78<spanclass=latexbold>(D)</span>910<spanclass=latexbold>(E)</span>1112<span class='latex-bold'>(A) </span> \frac{5}{8} \qquad <span class='latex-bold'>(B) </span> \frac{4}{5} \qquad <span class='latex-bold'>(C) </span> \frac{7}{8} \qquad <span class='latex-bold'>(D) </span> \frac{9}{10} \qquad <span class='latex-bold'>(E) </span> \frac{11}{12}