Question 526562
Guess and Check would be the best way to solve this problem.
Since a dime is worth 10 cents and a quarter is worth 25 cents, and there has to be 11 coins, We can just keep trying different things. 

1st attempt: 6(.25)+5(.10) =
             1.50+.50 = $2.00 (Not the answer)

2nd attempt: 5(.25)+6(.10) = 
             1.25+.60 = $1.85 (Not the answer)

3rd attempt: 4(.25)+7(.10) =
             1.00+.70 = $1.70 (The answer)

After guessing and checking, We now know that the answer is 4 quarters and 7 dimes.