2014 Cayley Problem 18

At the post office, Sonita bought some 2\,¢ stamps and she bought ten times as many 1\,¢ stamps as 2\,¢ stamps. She also bought some 5\,¢ stamps. She did not buy any other stamps. The total value of the stamps that she bought was 100\,¢. How many stamps did Sonita buy in total?

\textbf{(A)}\ 66\quad \textbf{(B)}\ 30\quad \textbf{(C)}\ 44\quad \textbf{(D)}\ 63\quad \textbf{(E)}\ 62

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.