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's suppose that the purse contains $x$ pennies. Since the purse also contains the same number of nickels and dimes, it contains $\frac{x}{5}$ nickels and $\frac{x}{10}$ dimes.
The total value of the pennies is $x$ cents, the total value of the nickels is $\frac{5x}{5}=x$ cents, and the total value of the dimes is $\frac{10x}{10}=x$ cents.
Adding up all the values, we know that $x+x+x=288$ cents. Simplifying, we get $3x=288$ cents.
Dividing both sides of the equation by 3, we find that $x=\boxed{96}$ cents or 96 pennies.