2024 Gauss 8 Problem 22

The ratio of the number of quarters (worth \$0.25 each) to the number of dimes (worth \$0.10 each) to the number of nickels (worth \$0.05 each) in a jar is 9 : 3 : 2. If the total value of the quarters and dimes is \$17.85, what is the total value of the nickels?

\textbf{(A)}\ \$0.45\quad \textbf{(B)}\ \$0.50\quad \textbf{(C)}\ \$0.70\quad \textbf{(D)}\ \$0.35\quad \textbf{(E)}\ \$0.55

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.