jmc

If $p$ is the number of pennies and $n$ is the number of nickels that Zachary used, then we are given $$\begin{array}{rl}p+n& =32\text{, and}\\ p+5n& =100.\end{array}$$ Subtracting the first equation from the second, we find $4n=68$ which implies $n=\boxed{17}$.