A caterer is hired to provide food for a private party consisting of 20 businessmen. She will be paid `$80` per hour and an additional `$40` tip if she serves all the food on time. If the caterer serves all the food on time, which of the following expressions can be used to determine how much the caterer earns, in dollars?

Options

A. `40x+(80+20)`, where x is the number of businessmen
B. `(80+20)x+40`, where x is the number of businessmen
C. `40x+80`, where x is the number of hours
D. `80x+40`, where x is the number of hours

Answer

To determine how much the caterer earns, we need to consider two main components of her payment:

1. **Hourly Rate**: The caterer is paid $80 per hour.
2. **Tip**: If she serves all the food on time, she receives an additional $40 tip.

Let’s denote the number of hours the caterer works as \( x \).

### Step-by-Step Solution:

1. **Calculate Earnings from Hourly Rate**:
- The caterer earns $80 for each hour she works. If she works for \( x \) hours, her earnings from the hourly rate can be expressed as:
\[ \text{Earnings from hourly rate} = 80x \]

2. **Add the Tip**:
- Since she serves all the food on time, she will receive an additional tip of $40. Therefore, her total earnings can be expressed as:
\[ \text{Total Earnings} = \text{Earnings from hourly rate} + \text{Tip} = 80x + 40 \]

Thus, the expression that can be used to determine how much the caterer earns in dollars is:
\[ \text{Total Earnings} = 80x + 40 \]
where \( x \) is the number of hours she works.

### Conclusion:
The correct expression for the caterer's earnings is \( 80x + 40 \), which corresponds to option **d**.