Chapter 5, Systems of Equations and Inequalities - Section 5.1 - Systems of Linear Equations in Two Variations - 5.1 Exercises - Page 447: 61

$5$ dimes and $9$ quarters.

Let $x$ be the number of dimes he had. Then the number of quarters is $14-x$. Then our equation is: $0.1x+0.25(14-x)=2.75\\0.1x+3.5-0.25x=2.75\\0.75=0.15x\\x=5$ Thus, he had $5$ dimes and $14-5=9$ quarters.