To find the number of baked goods Casey needs to sell to make a profit of exactly $100, we first express the profit as the total revenue minus total expenses.
Casey's revenue from selling baked goods is $220, and her expenses are $2.50 for each baked good sold. If she sells \( b \) baked goods, her total expenses would be \( 2.50b \).
The equation for profit \( P \) can be set up as:
\[
P = \text{Revenue} - \text{Expenses}
\]
Substituting in the numbers we have:
\[
100 = 220 - 2.50b
\]
This rearrangement shows that if her expenses (which increase with each baked good sold) exceed her revenue by $100, then she has made a profit of $100.
So, the correct answer is:
**B**: \( 220 - 2.50b = 100 \)