Hillary has eleven coins, all dimes and quarters. In total, the coins are worth 2 dollars and 15 cents. Write and solve a system of equations to determine how many quarters and how many dimes Hillary has.
Let's let $d$ represent the number of dimes Hillary has, and $q$ represent the number of quarters Hillary has. We can set up a system of two equations to represent the given information: \begin{align*}
d+q&=11 \qquad \text{(equation 1)}\\
10d+25q&=215 \qquad \text{(equation 2)}
\end{align*} Equation 1 represents the total number of coins, while equation 2 represents their total value in cents. Multiplying equation 1 by 10 gives $10d+10q=110$, so we can subtract this from equation 2 to find that $15q=105$. Dividing both sides of this equation by 15 gives $q=7$. Finally, substituting this value into equation 1 gives $d+7=11$, so $d=4$. Therefore, Hillary has $\boxed{4}$ dimes and $\boxed{7}$ quarters.