jmc

Let $n$ and $q$ represent the respective numbers of nickels and quarters. Since there are seven more nickels than quarters, we know that $q=n-7$. In cents, the amount of money Carol has is $5n+25q=455$. We substitute the expression of $q$ in terms of $n$ from the first equation into the second equation. $$\begin{array}{rl}5n+25(n-7)& =455\Rightarrow \\ n+5(n-7)& =91\Rightarrow \\ n+5n-35& =91\Rightarrow \\ 6n& =126\Rightarrow \\ n& =21\end{array}$$ Carol has $\boxed{21}$ nickels in her piggy bank.