Sure, let's break down the problem in a step-by-step manner to determine which expression represents the money that the group raises.
1. Define the Variables:
- Let [tex]\( n \)[/tex] be the number of bottles sold.
- The price per bottle they sell is [tex]$12.
- The advertising cost per bottle is $[/tex]5.
- There is an additional total fixed advertising cost of [tex]$40.
2. Calculate the Revenue from Selling \( n \) Bottles:
- The revenue from selling \( n \) bottles at $[/tex]12 per bottle is [tex]\( 12n \)[/tex].
3. Calculate the Total Advertising Cost:
- The advertising cost per bottle is [tex]$5, so for \( n \) bottles, the cost is \( 5n \).
- There is an additional fixed advertising cost of $[/tex]40.
4. Combine to Find the Net Money Raised:
- The total revenue from bottle sales is [tex]\( 12n \)[/tex].
- The total advertising cost is [tex]\( 5n + 40 \)[/tex].
- The money raised equals the total revenue minus the total advertising cost:
[tex]\[
\text{Money Raised} = 12n - (5n + 40)
\][/tex]
5. Simplify the Expression:
- Distribute the negative sign through the parentheses:
[tex]\[
\text{Money Raised} = 12n - 5n - 40
\][/tex]
- Combine like terms:
[tex]\[
\text{Money Raised} = (12 - 5)n - 40
\][/tex]
[tex]\[
\text{Money Raised} = 7n - 40
\][/tex]
Now let's match this expression with the given options:
A. [tex]\( 12n - 5 - 40 \)[/tex]
B. [tex]\( (12 - 5)n - 40 \)[/tex]
C. [tex]\( 12 - 5n - 40 \)[/tex]
D. [tex]\( 40 - (12 - 5)n \)[/tex]
After comparing, option B, [tex]\( (12 - 5)n - 40 \)[/tex], simplifies correctly to [tex]\( 7n - 40 \)[/tex].
Conclusion:
The expression [tex]\( (12 - 5)n - 40 \)[/tex] accurately represents the money that the group raises. Therefore, the correct answer is:
B. [tex]\( (12 - 5) n - 40 \)[/tex]
