Skip to main content

2019 AMC 10B Problem 1

Problem 1 of 25EasierArithmetic

Alicia had two containers. The first was 56\frac{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\frac{3}{4} full of water. What is the ratio of the volume of the smaller container to the volume of the larger container?

Answer choices

Show solution

Solution

Let the volumes of the first and second containers be FF and SS. The amount of water is both 56F\dfrac56F and 34S\dfrac34S, so 56F=34S\dfrac56F=\dfrac34S. Thus FS=3456=910\dfrac{F}{S}=\dfrac{\frac{3}{4}}{\frac{5}{6}}=\dfrac9{10}. Since the first container is smaller, the ratio of the smaller container to the larger container is 910\dfrac9{10}. Thus, D is the correct answer.
AoPS wiki

Tagged: fraction · ratio and proportion

More practice