Bill is starting a gourmet cookie business. He spent $123 on baking equipment, and he will spend an additional $7 per batch on ingredients. Bill will sell each batch of cookies for $10.

Question

How many batches of cookies must Bill sell for his sales to equal his expenses?
batches of cookies

Answer 1

To find out how many batches of cookies Bill must sell for his sales to equal his expenses, we can set up a simple equation.

Expenses:

• Initial cost of baking equipment: $123
• Variable cost per batch for ingredients: $7
• So, the total expense for \( x \) batches can be expressed as: \[ \text{Total Expenses} = 123 + 7x \]

Revenue:

• Revenue from selling each batch of cookies: $10
• Thus, the total revenue from selling \( x \) batches is: \[ \text{Total Revenue} = 10x \]

Setting Expenses equal to Revenue: To find the break-even point, we set the total expenses equal to total revenue: \[ 123 + 7x = 10x \]

Solving for \( x \):

1. Subtract \( 7x \) from both sides: \[ 123 = 10x - 7x \] \[ 123 = 3x \]
2. Divide both sides by 3: \[ x = \frac{123}{3} = 41 \]

Therefore, Bill must sell 41 batches of cookies for his sales to equal his expenses.