2001 Gauss 7 Problem 12

The ratio of the number of big dogs to the number of small dogs at a pet show is 3{:}17. There are 80 dogs, in total, at this pet show. How many big dogs are there?

\textbf{(A)}\ 12\quad \textbf{(B)}\ 68\quad \textbf{(C)}\ 20\quad \textbf{(D)}\ 24\quad \textbf{(E)}\ 6

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.