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

1 answer

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:

\[ 23p = 150 + 17p \]