Question

Casey earned $220 selling baked goods. Her expenses were $2.50 per baked good. Which equation can be used to find b, the number of baked goods Casey would have to sell in order to make a profit of exactly $100

Answer 1

To find the equation that represents Casey's situation, we first need to express her profit mathematically. Profit is calculated as total revenue minus total expenses.

Given:
- Casey's total earnings (revenue) from selling baked goods is $220.
- The cost (expenses) per baked good is $2.50.
- She wants to make a profit of exactly $100.

Let \( b \) represent the number of baked goods sold.

1. **Total Revenue**: This is the amount of money earned from selling \( b \) baked goods. It can be represented as:
\[
\text{Total Revenue} = 220
\]

2. **Total Expenses**: This is the cost per baked good times the number of baked goods sold:
\[
\text{Total Expenses} = 2.50b
\]

3. **Profit Equation**: Profit is given by the formula:
\[
\text{Profit} = \text{Total Revenue} - \text{Total Expenses}
\]
We want the profit to be $100, so the equation becomes:
\[
100 = 220 - 2.50b
\]

To isolate \( b \), rearranging the equation yields:
\[
2.50b = 220 - 100
\]
\[
2.50b = 120
\]
So, the equation that can be used to find \( b \) is:
\[
2.50b = 120
\]

Or equivalently:
\[
b = \frac{120}{2.50}
\]

Thus, the equation to use is either \( 2.50b = 120 \) or you can express it in terms of profit directly:
\[
\text{Profit} = 220 - 2.50b = 100
\]

Both are correct based on how you wish to express the relationship.