Three different chefs work together to prepare meals for 280 dinner guests. Each works at a different speed, and their combined output throughout the night is modeled by the equation 8x+4x+2x=280. If x is a positive integer, which of the following could 8x represent in the equation?

Options

A. The total meal output by the slowest chef , who made 40 meals
B. The total meal output by the fastest chef, who made 160 meals
C. The total meal output by the fastest chef, who made 80 meals
D. The difference between the output between the slowest and fastest chef, whihch would be 120 meals.

Answer

To solve the problem, we need to analyze the equation given for the combined output of the three chefs and determine what \(8x\) represents.

### Step-by-Step Solution:

1. **Understand the equation**: The equation given is:
\[ 8x + 4x + 2x = 280 \]
This represents the total number of meals prepared by the three chefs.

2. **Combine like terms**: Combine the terms on the left side of the equation:
\[ 14x = 280 \]

3. **Solve for \(x\)**: To find \(x\), divide both sides of the equation by 14:
\[ x = \frac{280}{14} = 20 \]

4. **Calculate the outputs for each chef**:
- The output of the fastest chef (represented by \(8x\)):
\[ 8x = 8 \times 20 = 160 \]
- The output of the middle chef (represented by \(4x\)):
\[ 4x = 4 \times 20 = 80 \]
- The output of the slowest chef (represented by \(2x\)):
\[ 2x = 2 \times 20 = 40 \]

5. **Identify what \(8x\) represents**: From the calculations, we see that \(8x\) represents the total meal output by the fastest chef, which is 160 meals.

6. **Evaluate the options**: We need to determine which of the provided options could represent \(8x\):
- a. The total meal output by the slowest chef who made 40 meals (Incorrect)
- b. The total meal output by the fastest chef who made 160 meals (Correct)
- c. The total meal output by the fastest chef who made 80 meals (Incorrect)
- d. The difference between the output between the slowest chef and the fastest chef which could be 120 meals (Incorrect)

### Conclusion:
The correct answer is option **b**: The total meal output by the fastest chef who made 160 meals.