Problem:
When a bucket is two-thirds full of water, the bucket and water weigh kilograms. When the bucket is one-half full of water the total weight is kilograms. In terms of and , what is the total weight in kilograms when the bucket is full of water?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Let be the weight of the bucket and let be the weight of the water in a full bucket. Then we are given that and . Hence , so . Thus . Finally, .
\section*{OR}
The difference between and is the weight of water that would fill of a bucket. So the weight of water that would fill of a bucket is . Therefore the weight of a bucket filled with water is .
The problems on this page are the property of the MAA's American Mathematics Competitions