2006 Gauss 8 Problem 21

Nathalie has some quarters, dimes and nickels. The ratio of the number of quarters to the number of dimes to the number of nickels that she has is 9 : 3 : 1. The total value of these coins is \$18.20. How many coins does Nathalie have?

\textbf{(A)}\ 130\quad \textbf{(B)}\ 117\quad \textbf{(C)}\ 98\quad \textbf{(D)}\ 91\quad \textbf{(E)}\ 140

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.