Let's analyze the problem step-by-step to understand how to calculate the money raised by the league.
1. Selling Price and Cost per Shirt:
- The league sells each shirt for \[tex]$14.
- The cost to make each shirt is \$[/tex]7.
- Therefore, the profit per shirt is [tex]\( \$14 - \$7 = \$7 \)[/tex].
2. Number of Shirts Sold:
- Let [tex]\( n \)[/tex] represent the number of shirts sold.
3. Total Profit from Selling [tex]\( n \)[/tex] Shirts:
- Since the profit per shirt is \[tex]$7, selling \( n \) shirts will give a total profit of \( 7n \).
4. Subtract Advertising Cost:
- The league spent \$[/tex]55 on advertising. This cost should be subtracted from the total profit.
- Therefore, the expression representing the total money raised after selling [tex]\( n \)[/tex] shirts, while accounting for the advertising cost, is [tex]\( 7n - 55 \)[/tex].
Now, let's identify the correct expression from the given options:
- A. [tex]\((14 - 7) n - 55\)[/tex] correctly simplifies to [tex]\(7n - 55\)[/tex].
- B. [tex]\(14 n - 7 - 55\)[/tex] does not correctly represent the process, as it subtracts fixed amounts incorrectly.
- C. [tex]\(55 - (14 - 7) n\)[/tex] incorrectly subtracts the profit from the advertising cost.
- D. [tex]\(14 - 7 n - 55\)[/tex] incorrectly calculates the profit and subtracts in an incorrect manner.
Therefore, the correct answer is:
[tex]\[ A. (14 - 7) n - 55 \][/tex]
which simplifies to:
[tex]\[ (7 \cdot n) - 55 \][/tex]
