There are a total of 95 coins, quarters and dimes, and the total is $15.35. How many dimes are there ?

Let $q$ be the number of quarters and $d$ be the number of dimes. Then 
\[q+d=95  (1)\]
and 
$$0.25q+0.10d=15.35   \Rightarrow  25q+10d=1535   (2).$$ From (1) we have $d=95-q$. Substituting this in (2) we get 
$$25q+10(95-q)=1535  \Rightarrow 15q=585 \Rightarrow q=39.$$
And hence $d=95-39=56.$