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

Which equation can you use to find p, the number of pillows Janelle must sell so that her costs equal her sales?
How many pillows must Janelle sell so that her costs equal her sales?
pillows

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 that represents her costs and her sales.

Cost Calculation:

1. Janelle has a fixed cost of the sewing machine: $150.
2. For each pillow, her variable costs (materials and shipping) are \( 12 + 5 = 17 \) dollars.

So, the total cost \( C \) for selling \( p \) pillows is: \[ C = 150 + 17p \]

Sales Calculation: Janelle sells each pillow for $23. Therefore, her total sales revenue \( R \) from selling \( p \) pillows is: \[ R = 23p \]

Setting Costs Equal to Sales: To find the number of pillows where her costs equal her sales, we set the cost equal to the revenue: \[ 150 + 17p = 23p \]

Solving the Equation: Now, we can solve the equation:

1. Subtract \( 17p \) from both sides: \[ 150 = 23p - 17p \] \[ 150 = 6p \]

2. Divide both sides by 6: \[ p = \frac{150}{6} = 25 \]

Therefore, Janelle must sell 25 pillows so that her costs equal her sales.