Question

1. bill and imani are selling pies for a school fundraiser. customers can buy blueberry pies and pumpkin pies. bill sold 6 blueberry pies and 6 pumpkin pies for a total of $180. imani sold 3 blueberry pies and 6 pumpkin pies for a total of $138. find the cost each of one blueberry pie and one pumpkin pie.

a) blueberry pie: $14, pumpkin pie: $16 b) blueberry pie: $12, pumpkin pie: $25
c) blueberry pie: $9, pumpkin pie: $19 d) blueberry pie: $22, pumpkin pie: $14
e) blueberry pie: $17, pumpkin pie: $11

Explanation:

Step1: Define Variables

Let \( b \) be the cost of a blueberry pie and \( p \) be the cost of a pumpkin pie.

Step2: Set Up Equations

From Bill's sales: \( 6b + 6p = 180 \) (divide by 6: \( b + p = 30 \))
From Imani's sales: \( 3b + 6p = 138 \) (divide by 3: \( b + 2p = 46 \))

Step3: Solve the System

Subtract the first simplified equation from the second:
\( (b + 2p) - (b + p) = 46 - 30 \)
\( p = 16 \)
Substitute \( p = 16 \) into \( b + p = 30 \):
\( b + 16 = 30 \)
\( b = 14 \)

Answer:

A) blueberry pie: $14, pumpkin pie: $16