2002 Gauss 7 Problem 23

Mark has a bag that contains 3 black marbles, 6 gold marbles, 2 purple marbles, and 6 red marbles. Mark adds a number of white marbles to the bag and tells Susan that if she now draws a marble at random from the bag, the probability of it being black or gold is \frac{3}{7}. The number of white marbles that Mark adds to the bag is

\textbf{(A)}\ 5\quad \textbf{(B)}\ 2\quad \textbf{(C)}\ 6\quad \textbf{(D)}\ 4\quad \textbf{(E)}\ 3

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 Gauss contests here.