Question

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.
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.