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.
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Revenue from selling pillows: Janelle sells the pillows for $23 each, so her total revenue from selling \( p \) pillows is \( 23p \).
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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:
\[ 23p = 150 + 17p \]