2025 Gauss 8 Problem 16

At Doggy Daycare, there is one dog for every bowl of food, two dogs for every bowl of water, and three dogs for every bowl of treats. Every dog gets a serving of food, water and treats. If there are a total of 77 bowls, how many dogs are there?

\textbf{(A)}\ 35\quad \textbf{(B)}\ 77\quad \textbf{(C)}\ 42\quad \textbf{(D)}\ 11\quad \textbf{(E)}\ 24

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.