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.
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Total Revenue: This is the amount of money earned from selling \( b \) baked goods. It can be represented as: \[ \text{Total Revenue} = 220 \]
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Total Expenses: This is the cost per baked good times the number of baked goods sold: \[ \text{Total Expenses} = 2.50b \]
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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.
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