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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: $$\begin{array}{rl}3p+e& =124\\ 5p+e& =182\end{array}$$ Subtracting the first equation from the second gives $2p=58$, or $p=29$. Thus, the cost of a pencil is $\boxed{29}$ cents.