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.

Question

p + q = 28. p + 25 q = 76.
p + q = 28. 25 p + q = 76.
p + q = 76. p + 25 q = 28.
p + q = 76. 25 p + q = 28.

Answer 1

To find a system of equations that relates the number of pennies and quarters Clara has, we can set up the following equations based on the information given:

1. The total number of coins (pennies + quarters) is 28.

   • This can be expressed as: \[ p + q = 28 \]

2. The total value of the coins is 76 cents. Since each penny is worth 1 cent and each quarter is worth 25 cents, the total value can be expressed as:

   • This can be formulated as: \[ p + 25q = 76 \]

Thus, the correct system of equations representing the situation is: \[ \begin{align*}

1. & \quad p + q = 28 \
2. & \quad p + 25q = 76 \end{align*} \]

So, the answer is: p + q = 28. p + 25 q = 76.