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.
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?
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