To determine the profit, we need to subtract the cost [tex]\( C \)[/tex] from the given revenue expressions. Let's go through the steps for each of the given revenue expressions.
### Revenue Expressions and Their Corresponding Profit Expressions
1. Revenue: [tex]\( 3x - 260 \)[/tex]
- Profit Calculation: Profit is given by subtracting the cost from the revenue:
[tex]\[
\text{Profit} = (3x - 260) - C
\][/tex]
Simplifying this, we get:
[tex]\[
\text{Profit} = 3x - 260 - C
\][/tex]
2. Revenue: [tex]\( 3x + 140 \)[/tex]
- Profit Calculation: Profit is given by subtracting the cost from the revenue:
[tex]\[
\text{Profit} = (3x + 140) - C
\][/tex]
Simplifying this, we get:
[tex]\[
\text{Profit} = 3x + 140 - C
\][/tex]
3. Revenue: [tex]\( 5x - 260 \)[/tex]
- Profit Calculation: Profit is given by subtracting the cost from the revenue:
[tex]\[
\text{Profit} = (5x - 260) - C
\][/tex]
Simplifying this, we get:
[tex]\[
\text{Profit} = 5x - 260 - C
\][/tex]
4. Revenue: [tex]\( 5x + 140 \)[/tex]
- Profit Calculation: Profit is given by subtracting the cost from the revenue:
[tex]\[
\text{Profit} = (5x + 140) - C
\][/tex]
Simplifying this, we get:
[tex]\[
\text{Profit} = 5x + 140 - C
\][/tex]
### Summary
So, the expressions for the profit are:
1. [tex]\( \text{Profit} = 3x - 260 - C \)[/tex]
2. [tex]\( \text{Profit} = 3x + 140 - C \)[/tex]
3. [tex]\( \text{Profit} = 5x - 260 - C \)[/tex]
4. [tex]\( \text{Profit} = 5x + 140 - C \)[/tex]
These are the expressions that represent the profit for each of the given revenue scenarios after subtracting the cost [tex]\( C \)[/tex].
