To find the bill for lunch before the tip was added, we start with the information that the tip amount was $2.75, which corresponds to 20% of the bill.
To calculate the total bill (let's call it \( B \)), we can use the formula for calculating tips:
\[ \text{Tip} = \text{Bill} \times \text{Tip Rate} \]
In this case, we know:
- Tip = $2.75
- Tip Rate = 20% = 0.20
Thus, we can set up the equation:
\[ 2.75 = B \times 0.20 \]
To solve for \( B \):
\[ B = \frac{2.75}{0.20} \] \[ B = \frac{2.75}{0.2} = 13.75 \]
Therefore, the bill for lunch before the tip was added is $13.75.