Problem:
Alicia had two containers. The first was 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 full of water. What is the ratio of the volume of the smaller container to the volume of the larger container?
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Solution:
Let be the volume of the first container and the volume of the second container. Then
The problems on this page are the property of the MAA's American Mathematics Competitions