Question

tickets to a basketball game can be ordered online for a set price per ticket plus a $5.50 service fee. the total cost in dollars for ordering 5 tickets is $108.00. which linear function represents c, the total cost, when x tickets are ordered? (a service fee is a single fee applied to the total, no matter the number of tickets purchased).
$c(x) = 5.50 + 20.50x$
$c(x) = 5.50 + 21.60x$
$c(x) = 5.50x + 20.50$
$c(x) = 5.50x + 21.60$

Explanation:

Step1: Define the linear function structure

A linear function for total cost \( c(x) \) will have the form \( c(x)= \text{service fee} + (\text{price per ticket}) \times x \). The service fee is a one - time fee of \( \$5.50 \), so the function is \( c(x)=5.50 + px \), where \( p \) is the price per ticket.

Step2: Calculate the price per ticket

We know that when \( x = 5 \) tickets are ordered, the total cost \( c(5)=108.00 \). Substitute into the equation \( c(x)=5.50+px \):
\[

$$\begin{align*} 108.00&=5.50 + p\times5\\ 108.00 - 5.50&=5p\\ 102.50&=5p\\ p&=\frac{102.50}{5}\\ p& = 20.50 \end{align*}$$

\]

Step3: Write the linear function

Now that we know the price per ticket \( p = 20.50 \) and the service fee is \( 5.50 \), the linear function for the total cost \( c(x) \) when \( x \) tickets are ordered is \( c(x)=5.50 + 20.50x \).

Answer:

\( c(x)=5.50 + 20.50x \) (the first option among the given choices)