Let's solve this step-by-step:
1. Selling Price: The group plans to sell each hat at [tex]\(\$12\)[/tex].
2. Cost to Make Each Hat: It costs [tex]\(\$6\)[/tex] to make each hat.
3. Profit Per Hat: To find the profit per hat, we subtract the cost to make each hat from the selling price. So:
[tex]\[
\text{Profit per hat} = \$12 - \$6 = \$6
\][/tex]
4. Number of Hats Sold: Let [tex]\(n\)[/tex] represent the number of hats sold.
5. Total Profit from Selling [tex]\(n\)[/tex] Hats: To find the total money raised from selling [tex]\(n\)[/tex] hats, we multiply the profit per hat by the number of hats sold:
[tex]\[
\text{Total Profit} = \$6 \times n = 6n
\][/tex]
6. Advertising Cost: They spent [tex]\(\$50\)[/tex] on advertising.
7. Total Money Raised: To find the total money raised, we subtract the advertising cost from the total profit:
[tex]\[
\text{Total Money Raised} = 6n - 50
\][/tex]
So, the expression that represents the money that the group raises is:
[tex]\[
6n - 50
\][/tex]
Examining the given options:
- Option A: [tex]\(12 - 6n - 50\)[/tex]: This subtracts [tex]\(6n\)[/tex] after subtracting 50, which is incorrect.
- Option B: [tex]\((12 - 6)n - 50\)[/tex]: This simplifies to [tex]\(6n - 50\)[/tex], which matches our derived expression.
- Option C: [tex]\(12n - 6 - 50\)[/tex]: This simplifies to [tex]\(12n - 56\)[/tex], which is incorrect.
Therefore, the correct expression is:
[tex]\[ (12 - 6)n - 50 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{(12 - 6)n - 50} \][/tex]
