To find the correct linear function representing the total cost [tex]\( c \)[/tex] when ordering [tex]\( x \)[/tex] tickets, given that the total cost for 5 tickets is \[tex]$108.00 and there is a \$[/tex]5.50 service fee, follow these steps:
1. Identify Known Values:
- Service fee (fixed): \[tex]$5.50
- Total cost for 5 tickets: \$[/tex]108.00
- Number of tickets: 5
2. Setup the Equation:
The total cost for 5 tickets includes the service fee and the cost per ticket. Let [tex]\( p \)[/tex] be the price of one ticket. The equation for the total cost when buying 5 tickets is:
[tex]\[
5p + 5.50 = 108.00
\][/tex]
3. Solve for [tex]\( p \)[/tex] (price per ticket):
Subtract the service fee from the total cost:
[tex]\[
5p = 108.00 - 5.50 = 102.50
\][/tex]
Then, divide by 5 to find the price per ticket:
[tex]\[
p = \frac{102.50}{5} = 20.50
\][/tex]
4. Form the Linear Function:
The total cost [tex]\( c \)[/tex] when ordering [tex]\( x \)[/tex] tickets can be expressed as:
[tex]\[
c(x) = 5.50 + 20.50x
\][/tex]
This linear function accounts for the fixed service fee of \[tex]$5.50 and the price per ticket of \$[/tex]20.50.
So, the correct linear function representing [tex]\( c \)[/tex], the total cost when ordering [tex]\( x \)[/tex] tickets, is:
[tex]\[
c(x) = 5.50 + 20.50x
\][/tex]
Therefore, the answer is:
[tex]\[
c(x) = 5.50 + 20.50x
\][/tex]
