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?

23p=150+12p+5p

23+12p=150+5p

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 total revenue and total costs.

1. **Revenue from selling pillows:** Janelle sells the pillows for $23 each, so her total revenue from selling \( p \) pillows is \( 23p \).

2. **Costs:** Janelle has a fixed cost for the sewing machine, which is $150, and her variable costs for materials and shipping for each pillow, which is \( 12 + 5 = 17 \) dollars per pillow. Thus, her total costs for \( p \) pillows are \( 150 + 17p \).

Now, we set the total revenue equal to the total costs:

\[
23p = 150 + 17p
\]

This equation can be used to find \( p \).

So, the correct equation that you can use to find the number of pillows is:

**\( 23p = 150 + 12p + 5p \)**

This is the correct representation of her situation.

When you combine the costs on the right side, it simplifies to:

\[
23p = 150 + 17p
\]

Thus, to summarize, the equation to find \( p \) is:

\[
23p = 150 + 17p
\]