2017 Cayley Problem 15

A bag contains red, blue and purple marbles, and does not contain any other marbles. The ratio of the number of red marbles to the number of blue marbles is 4 : 7. The ratio of the number of blue marbles to the number of purple marbles is 2 : 3. There are 32 red marbles in the bag. In total, how many marbles are there in the bag?

\textbf{(A)}\ 162\quad \textbf{(B)}\ 129\quad \textbf{(C)}\ 176\quad \textbf{(D)}\ 164\quad \textbf{(E)}\ 172

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.