A change purse contains an equal number of pennies, nickels, and dimes. The total value of the coins is 288 cents. How many pennies does the purse contain?
Let $p$ be the number of pennies, nickels, and dimes in the purse. The total value of the pennies is $p$ cents, and the total value of the nickels is $5p$ cents, and the total value of the dimes is $10p$ cents. Hence, \[p + 5p + 10p = 288,\]which simplifies to $16p = 288$. Then $p = \boxed{18}$.
