AMC 12 2012a Problem 5

A fruit salad consists of blueberries, raspberries, grapes, and cherries. The fruit salad has a total of $280$ pieces of fruit. There are twice as many raspberries as blueberries, three times as many grapes as cherries, and four times as many cherries as raspberries. How many cherries are there in the fruit salad?

\textbf{(A)}\ 8 \textbf{(B)}\ 16 \textbf{(C)}\ 25 \textbf{(D)}\ 64 \textbf{(E)}\ 96