2019 AMC 12B Problem 1

Below is the professionally curated solution for Problem 1 of the 2019 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2019 AMC 12B solutions, or check the answer key.

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Concepts:ratio and proportion fraction

Difficulty rating: 880

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?

$\dfrac{5}{8}$

$\dfrac{4}{5}$

$\dfrac{7}{8}$

$\dfrac{9}{10}$

$\dfrac{11}{12}$

Solution:

The volume of water is the same before and after, so $\dfrac{5}{6}V_1=\dfrac{3}{4}V_2.$

Then $\dfrac{V_1}{V_2}=\dfrac{3/4}{5/6}=\dfrac{3}{4}\cdot\dfrac{6}{5}=\dfrac{9}{10}.$

Thus, D is the correct answer.

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