Let's break the problem down step-by-step:
1. Determine the debt for each ticket:
Each ticket costs [tex]$ -\$[/tex] 32[tex]$. Since the tickets are pre-ordered and not paid for, this represents a debt per ticket.
2. Calculate the total debt for the tickets:
The total number of tickets is 12. So, we need to find the overall debt for these 12 tickets by multiplying:
\[
12 \text{ tickets} \times -\$[/tex] 32 \text{ (per ticket)} = -\[tex]$ 384
\]
3. Include the additional fee:
The tour company adds a $[/tex] \[tex]$ 20$[/tex] fee for the entire order. This fee is added to the total debt.
4. Calculate the total debt including the fee:
We add the fee to the total ticket debt:
[tex]\[
-\$ 384 \text{ (total ticket debt)} + \$ 20 \text{ (fee)} = -\$ 364
\][/tex]
The final value, representing the total debt including the fee, is:
[tex]\[
- \$ 364
\][/tex]
So, among the given choices, the correct representation of the total debt is:
[tex]\[
- \$ 364
\][/tex]
