Question

1. gabriella and scott are selling pies for a school fundraiser. customers can buy cherry pies and pumpkin pies. gabriella sold 4 cherry pies and 1 pumpkin pie for a total of $64. scott sold 4 cherry pies and 13 pumpkin pies for a total of $256. find the cost each of one cherry pie and one pumpkin pie.

Explanation:

Step1: Define Variables

Let \( c \) be the cost of one cherry pie and \( p \) be the cost of one pumpkin pie.

Step2: Set Up Equations

From Gabriella's sales: \( 4c + p = 64 \) (Equation 1)
From Scott's sales: \( 4c + 13p = 256 \) (Equation 2)

Step3: Subtract Equations

Subtract Equation 1 from Equation 2:
\( (4c + 13p) - (4c + p) = 256 - 64 \)
\( 12p = 192 \)

Step4: Solve for \( p \)

\( p = \frac{192}{12} = 16 \)

Step5: Solve for \( c \)

Substitute \( p = 16 \) into Equation 1:
\( 4c + 16 = 64 \)
\( 4c = 64 - 16 = 48 \)
\( c = \frac{48}{4} = 12 \)

Answer:

The cost of one cherry pie is \$12 and one pumpkin pie is \$16.