To determine the cost of one ticket, we need to look at the differences in costs and the differences in the number of tickets purchased and use those to work out the cost per ticket. Let's break it down step by step:
1. Identify Ticket Numbers and Total Costs:
- For 3 tickets, the total cost is \[tex]$46.50.
- For 5 tickets, the total cost is \$[/tex]67.50.
- For 8 tickets, the total cost is \[tex]$99.00.
2. Calculate the Differences:
- Difference in total cost between 5 tickets and 3 tickets:
\[
\Delta \text{Cost}_{5-3} = \$[/tex]67.50 - \[tex]$46.50 = \$[/tex]21.00
\]
- Difference in total cost between 8 tickets and 5 tickets:
[tex]\[
\Delta \text{Cost}_{8-5} = \$99.00 - \$67.50 = \$31.50
\][/tex]
- Difference in number of tickets between 5 and 3:
[tex]\[
\Delta \text{Tickets}_{5-3} = 5 - 3 = 2
\][/tex]
- Difference in number of tickets between 8 and 5:
[tex]\[
\Delta \text{Tickets}_{8-5} = 8 - 5 = 3
\][/tex]
3. Determine the Cost Per Ticket:
- From 3 to 5 tickets (2 additional tickets), the cost increased by \[tex]$21.00:
\[
\text{Cost per ticket}_{3-5} = \frac{\$[/tex]21.00}{2} = \[tex]$10.50
\]
- From 5 to 8 tickets (3 additional tickets), the cost increased by \$[/tex]31.50:
[tex]\[
\text{Cost per ticket}_{5-8} = \frac{\$31.50}{3} = \$10.50
\][/tex]
4. Confirm Consistency:
- Both calculations give the same cost per ticket:
[tex]\[
\text{Cost per ticket} = \$10.50
\][/tex]
Thus, the cost of one ticket is:
D. \$10.50
