2007 Cayley Problem 18

There are a certain number of red balls, green balls and blue balls in a bag. Of the balls in the bag, \frac{1}{3} are red and \frac{2}{7} are blue. The number of green balls in the bag is 8 less than twice the number of blue balls. The number of green balls in the bag is

\textbf{(A)}\ 12\quad \textbf{(B)}\ 16\quad \textbf{(C)}\ 20\quad \textbf{(D)}\ 24\quad \textbf{(E)}\ 28

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.