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? Choices: (A)23p = 150 + 12p + 5p (B)23 + 12p = 150 + 5p How many pillows must Janelle sell so that her costs equal her sales? ____ pillows

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?   Choices: (A)23p = 150 + 12p + 5p (B)23 + 12p = 150 + 5p  How many pillows must Janelle sell so that her costs equal her sales?   ____ pillows

Bytelearn · Accepted Answer

Set Up Equation: To find the break-even point where Janelle's costs equal her sales, we need to set up an equation where the total cost is equal to the total sales. The total cost includes the fixed cost of the sewing machine and the variable costs of materials and shipping for each pillow. The total sales are the price at which she sells each pillow multiplied by the number of pillows sold, p.Cost and Sales Breakdown: The fixed cost for the sewing machine is $150. The variable cost for each pillow is $12 for materials and $5 for shipping, which adds up to $12 + $5 = $17 per pillow. The sale price for each pillow is $23. So, the equation representing the total cost (C) is C = 150 + 17p, and the equation representing the total sales (S) is S = 23p.Equation for Break-Even Point: To find the number of pillows Janelle must sell to break even, we set the total cost equal to the total sales: 150 + 17p = 23p. This is the correct equation to represent the situation, which corresponds to choice (A) 23p = 150 + 12p + 5p.Isolate Variable in Equation: Now we solve for p. Subtract 17p from both sides of the equation to isolate the variable on one side: 150 + 17p - 17p = 23p - 17p, which simplifies to 150 = 6p.Solve for Number of Pillows: Divide both sides of the equation by 6 to solve for p: 150 / 6 = 6p / 6, which simplifies to 25 = p.

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