To determine the correct linear function representing the total cost [tex]\( c \)[/tex] when [tex]\( x \)[/tex] tickets are ordered, we need to follow these steps:
1. Define Known Values:
- The number of tickets, [tex]\( x \)[/tex], is 5.
- The total cost for 5 tickets is \[tex]$108.00.
- The service fee is \$[/tex]5.50.
2. Find the Cost Per Ticket:
- The total cost consists of the cost of the tickets plus the service fee:
[tex]\[
\text{total\_cost} = (\text{cost\_per\_ticket} \times \text{num\_tickets}) + \text{service\_fee}
\][/tex]
For our specific known values:
[tex]\[
108.00 = (\text{cost\_per\_ticket} \times 5) + 5.50
\][/tex]
- Solving for [tex]\(\text{cost\_per\_ticket}\)[/tex]:
[tex]\[
108.00 - 5.50 = \text{cost\_per\_ticket} \times 5
\][/tex]
[tex]\[
102.50 = \text{cost\_per\_ticket} \times 5
\][/tex]
[tex]\[
\text{cost\_per\_ticket} = \frac{102.50}{5}
\][/tex]
[tex]\[
\text{cost\_per\_ticket} = 20.50
\][/tex]
3. Constructing the Linear Function:
- We need to include both the per-ticket cost and the fixed service fee in our function. The total cost when [tex]\( x \)[/tex] tickets are ordered can be expressed as:
[tex]\[
c(x) = \text{service\_fee} + (\text{cost\_per\_ticket} \times x)
\][/tex]
Substituting the values we have:
[tex]\[
c(x) = 5.50 + 20.50x
\][/tex]
4. Match the Function with Given Choices:
- The correct function is:
[tex]\[
c(x) = 5.50 + 20.50x
\][/tex]
Hence, the linear function that represents [tex]\( c \)[/tex], the total cost, when [tex]\( x \)[/tex] tickets are ordered, is:
[tex]\[ c(x) = 5.50 + 20.50x \][/tex]
So, the correct choice is:
[tex]\[ c(x) = 5.50 + 20.50x \][/tex]
