A jar contains 20 coins, all dimes and quarters, worth a total of $3.65. How many quarters are in the jar?

Let $q$ be the number of quarters, so there are $20-q$ dimes. The value in dollars is $0.25q+0.10(20-q)=3.65$, which simplifies to $0.15q+2=3.65$, so $0.15q=1.65$ and $q=11$, choice J. Check: $11$ quarters are worth $2.75 and $9$ dimes are worth $0.90, a total of $3.65. Choice F ($9$) is the number of dimes, not quarters. Choice G ($16$) gives $4.00 + $0.40 = $4.40. Choice H ($14$) gives $3.50 + $0.60 = $4.10. Neither equals $3.65.