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 first container to the volume of the second container?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let the first jar's volume be and the second's be . It is given that
We find that
We already know that this is the ratio of the smaller to the larger volume because it is less than 1.
An alternate solution is to substitute an arbitrary maximum volume for the first container — let’s say 72, so there was a volume of 60 in the first container, and then the second container also has a volume of 60, so you get
Thus the answer is
The problems on this page are the property of the MAA's American Mathematics Competitions