Clara has pennies and quarters in her purse. She counts a total of 28 coins. If the total value of the coins is 76 cents, which system of equations can be used to determine the number of pennies and the number of quarters? Assume p represents the number of pennies and q represents the number of quarters.

This may need to be double checked but:

If there are 28 coins in total, then the first equation would be

P+Q=28

If the coins add up to 76 cents then you take 25Q (because quarters equal 25 cents) + 1P (because pennies equal 1 cent)

And so your second equation is 25Q+1P=76

So both of your equations are:

p+q=28

25q+1p=76