# Problem #1477

 1477 When a bucket is two-thirds full of water, the bucket and water weigh $a$ kilograms. When the bucket is one-half full of water the total weight is $b$ kilograms. In terms of $a$ and $b$, what is the total weight in kilograms when the bucket is full of water? $\textbf{(A)}\ \frac23a + \frac13b\qquad \textbf{(B)}\ \frac32a - \frac12b\qquad \textbf{(C)}\ \frac32a + b \qquad \textbf{(D)}\ \frac32a + 2b\qquad \textbf{(E)}\ 3a - 2b$ This problem is copyrighted by the American Mathematics Competitions.
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