2020 Cayley Problem 17

Carley made treat bags. Each bag contained exactly 1 chocolate, 1 mint, and 1 caramel. The chocolates came in boxes of 50. The mints came in boxes of 40. The caramels came in boxes of 25. Carley made no incomplete treat bags and there were no unused chocolates, mints or caramels. What is the minimum total number of boxes that Carley could have bought?

\textbf{(A)}\ 19\quad \textbf{(B)}\ 17\quad \textbf{(C)}\ 44\quad \textbf{(D)}\ 25\quad \textbf{(E)}\ 9

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.