I recently happened upon a problem. I have produced a solution, however, I am not sure whether it is acceptable or not. Here is the problem:

$\displaystyle a$ apples weigh the same as $\displaystyle b$ bananas. $\displaystyle B$ bananas weigh the same as $\displaystyle C$ cherries. How many cherries weigh the same as $\displaystyle A$ apples?

I believe the solution to be $\displaystyle A$ apples$\displaystyle =\frac{AbC}{aB}$ cherries. The problem is that I am not sure whether it is acceptable to have $\displaystyle A$ on both sides of the equation. I have asked a few individuals and opinions vary. Is the solution acceptable?

Thank you. All help on this problem is appreciated.