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?

Answer 1

To determine how many batches of cookies Bill must sell for his sales to equal his expenses, we can start by identifying Bill's total expenses and total revenue from selling the cookies.

1. Fixed costs: Bill has a one-time expense for baking equipment of $123.

2. Variable costs: Each batch of cookies costs him an additional $7. If he bakes \( x \) batches, his total cost for ingredients will be \( 7x \).

3. Total expenses: This is calculated as the sum of the fixed costs and the variable costs: \[ \text{Total expenses} = 123 + 7x \]

4. Revenue from sales: Bill sells each batch for $10, so the revenue from selling \( x \) batches will be: \[ \text{Total revenue} = 10x \]

5. Setting up the equation: To find out how many batches he needs to sell for his sales to equal his expenses, we set the total revenue equal to the total expenses: \[ 10x = 123 + 7x \]

6. Solving the equation: \[ 10x - 7x = 123 \] \[ 3x = 123 \] \[ x = \frac{123}{3} = 41 \]

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