Let's denote the number of pennies, nickels, and dimes each as $x$.

Step-by-step solution:

1. Value of the pennies: Each penny is worth 1 cent, so the total value of the pennies is: $1 \cdot x = x \, \text{cents}.$

2. Value of the nickels: Each nickel is worth 5 cents, so the total value of the nickels is: $5 \cdot x \, \text{cents}.$

3. Value of the dimes: Each dime is worth 10 cents, so the total value of the dimes is: $10 \cdot x \, \text{cents}.$

4. Total value of all the coins: The total value of the pennies, nickels, and dimes combined is: $x + 5x + 10x = 16x \, \text{cents}.$ According to the problem, this total is 448448 cents: $16x = 448448.$

5. Solve for $x$: To find $x$, divide both sides of the equation by 16: $x = \frac{448448}{16} = 28028.$

Thus, the purse contains 28,028 pennies.

Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How many nickels does the purse contain?
2. What is the total number of coins in the purse?
3. How much would the total value be if there were twice as many pennies?
4. What is the total value of the nickels alone?
5. If the number of dimes is halved, how does that affect the total value?

Tip: When dealing with multiple items of different values, start by assigning variables to quantities and form equations based on their total value.