Problem C

Counting Coins

Inaaya has a jar of coins containing only nickels, dimes, and quarters. A nickel is worth \(5\) cents, a dime is worth \(10\) cents, a quarter is worth \(25\) cents, and a dollar is worth \(100\) cents.

The ratio of the number of quarters to the number of dimes to the number of nickels in the jar is \(9:3:1\). The total value of all the coins in the jar is \(\$18.20\). How many coins does Inaaya have in her jar?

**Themes:** Algebra, Number Sense