To determine the expression that represents the money raised by the community sports league, let's break down the given information step-by-step:
1. Selling Price per Shirt: The league plans to sell each shirt for \[tex]$15.
2. Cost per Shirt: Each shirt costs \$[/tex]8 to make.
3. Advertising Cost: They spent \[tex]$55 on advertising.
4. Variable: Let's use \( n \) to represent the number of shirts sold.
### Step-by-Step Calculation:
1. Profit per Shirt:
- The profit is the selling price minus the cost price per shirt.
- Profit per shirt = \$[/tex]15 (selling price) - \[tex]$8 (cost price) = \$[/tex]7 per shirt.
2. Total Profit for [tex]\( n \)[/tex] Shirts:
- If the league sells [tex]\( n \)[/tex] shirts, the total profit from selling [tex]\( n \)[/tex] shirts is [tex]\( 7n \)[/tex].
- This is because each shirt gives a profit of \[tex]$7, and selling \( n \) shirts would give \( 7n \).
3. Subtract Advertising Cost:
- The profit from selling \( n \) shirts is \( 7n \).
- The total money raised must account for the advertising expense of \$[/tex]55.
- Therefore, the total money raised = [tex]\( 7n \)[/tex] (total profit) - \$55 (advertising cost).
Putting it all together, the expression that represents the money raised is:
[tex]\[ 7n - 55 \][/tex]
Now let’s compare it to the given options:
- Option A: [tex]\((15 - 8)n - 55\)[/tex]
- Breaking it down, (15 - 8) is 7, so this translates to [tex]\( 7n - 55 \)[/tex].
- Hence, Option A is correct.
- Option B: [tex]\(15 - 8n - 55\)[/tex]
- This expression incorrectly subtracts 8 times the number of shirts (8n) from 15, and then subtracts 55.
- This does not match our derived expression.
- Option C: [tex]\(55 - (15 - 8)n\)[/tex]
- This expression incorrectly subtracts the total profit from 55 instead of subtracting 55 from the total profit.
- This does not match our derived expression.
- Option D: [tex]\(15n - 8 - 55\)[/tex]
- This expression incorrectly ends with subtracting 8 and 55 directly from 15n without proper profit calculations.
- This does not match our derived expression.
Thus, the correct expression is:
[tex]\[ \boxed{(15 - 8)n - 55} \][/tex]
Or simplified,
[tex]\[ \boxed{7n - 55} \][/tex]
So, the correct option is [tex]\( \textbf{A} \)[/tex].
