To find an equation that can be used to solve for \( b \), the number of baked goods Casey needs to sell to make a profit of $100, we can start by looking at the components of Casey's earnings and expenses.
Casey's total earnings from selling baked goods is $220. Her expenses for selling each baked good is $2.50. Therefore, if she sells \( b \) baked goods, her total expenses will be \( 2.50b \).
To calculate profit, we use the formula:
\[ \text{Profit} = \text{Total Earnings} - \text{Total Expenses} \]
In this case, Casey wants to make a profit of $100, so we can set up the following equation:
\[ \text{Profit} = 220 - 2.50b \]
Setting this equal to $100 (the desired profit):
\[ 220 - 2.50b = 100 \]
Now, we can solve for \( b \):
- Subtract 220 from both sides:
\[ -2.50b = 100 - 220 \]
\[ -2.50b = -120 \]
- Divide both sides by -2.50 to isolate \( b \):
\[ b = \frac{-120}{-2.50} \]
\[ b = 48 \]
Therefore, Casey needs to sell 48 baked goods to make a profit of $100.
As a final summary, the equation that can be used to solve for \( b \) is:
\[ 220 - 2.50b = 100 \]
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