Janelle plans to make pillows and sell them online for $23 each. She already bought a sewing machine for $150. Additionally, for each pillow, she will need to spend $12 on materials and $5 on shipping.

Question

Which equation can you use to find p, the number of pillows Janelle must sell so that her costs equal her sales?

Answer 1

To find the number of pillows \( p \) that Janelle must sell so that her costs equal her sales, we need to set up an equation based on her expenses and her income from selling the pillows.

1. Expenses (Cost):

   • The initial cost of the sewing machine is $150.
   • The cost for materials for each pillow is $12.
   • The shipping cost for each pillow is $5.

   Thus, the total cost for \( p \) pillows can be expressed as: \[ \text{Total Cost} = 150 + (12 + 5)p = 150 + 17p \]

2. Sales (Revenue):

   • Janelle sells each pillow for $23.

   Therefore, the total revenue from selling \( p \) pillows is: \[ \text{Total Revenue} = 23p \]

3. Setting up the equation: To find the number of pillows \( p \) where her costs equal her sales, we set the total cost equal to the total revenue: \[ 150 + 17p = 23p \]

This equation can be used to find the value of \( p \) where Janelle's costs equal her sales.