2009 AMC 12B Problem 8

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

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.