Three pencils and a jumbo eraser cost $\$1.24$. Five pencils and a jumbo eraser cost $\$1.82$. No prices include tax. In cents, what is the cost of a pencil?
Call the price of a pencil $p$ and the price of a jumbo eraser $e$, in terms of cents. We can use the following system of equations to represent the information given: \begin{align*}
3p + e &= 124 \\
5p + e &= 182 \\
\end{align*} Subtracting the first equation from the second gives $2p = 58$, or $p = 29$. Thus, the cost of a pencil is $\boxed{29}$ cents.