2008 Fermat Problem 9

Beshmi invested \frac{1}{5} of her savings in Company X, 42\% in Company Y, and the remainder in Company Z. If Beshmi invested \$10\,500 in Company Y, how much did she invest in Company Z?

\textbf{(A)}\ \$25\,000\quad \textbf{(B)}\ \$15\,500\quad \textbf{(C)}\ \$14\,000\quad \textbf{(D)}\ \$9500\quad \textbf{(E)}\ \$5000

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 Fermat contests here.