Let's break the problem down step-by-step:
1. Identify the revenue expression:
- According to the problem statement, revenue is given by the expression [tex]\(3x - 260\)[/tex].
2. Identify the cost expression:
- We are given that the cost is [tex]\(x - 60\)[/tex].
3. Calculate the profit as the difference between revenue and cost:
- Profit = Revenue - Cost
So, we can express this mathematically as:
[tex]\[ \text{Profit} = (3x - 260) - (x - 60) \][/tex]
4. Simplify the profit expression:
First, distribute the negative sign to both terms inside the parentheses for the cost:
[tex]\[ \text{Profit} = 3x - 260 - x + 60 \][/tex]
Next, combine like terms (the terms containing [tex]\(x\)[/tex] and the constants together):
[tex]\[ \text{Profit} = (3x - x) + (-260 + 60) \][/tex]
[tex]\[ \text{Profit} = 2x - 200 \][/tex]
Therefore, the expression that represents the profit is:
[tex]\[ 2x - 200 \][/tex]
None of the options you provided match this result precisely. Double-checking the options, it seems there may have been an error in the options listed or a misinterpretation of the expressions provided. Please ensure the problem statement and options are correct. If the options given were intended to be correct, then there might be a clerical error in them.
