Question

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.
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.