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

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

GPT-4o mini · 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: $$ 23p = 150 + 17p $$