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).

Question

c(x) = 5.50 + 20.50x
c(x) = 5.50x + 20.50
c(x) = 5.50 + 21.60x
c(x) = 5.50x + 21.60

Answer 1

To find the linear function that represents the total cost \( c \) when \( x \) tickets are ordered, we are given the following:

1. There is a service fee of $5.50.
2. The total cost for 5 tickets is $108.00.

Let \( p \) be the price of one ticket. The cost for ordering \( x \) tickets plus the service fee will be represented as:

\[ c(x) = px + 5.50 \]

Given that the cost for 5 tickets is $108.00, we can write the equation:

\[ c(5) = 5p + 5.50 = 108 \]

Now we can solve for \( p \):

1. Subtract $5.50 from both sides: \[ 5p = 108 - 5.50 \] \[ 5p = 102.50 \]

2. Divide by 5: \[ p = \frac{102.50}{5} = 20.50 \]

Now we can substitute \( p \) back into our cost function:

\[ c(x) = 20.50x + 5.50 \]

This gives us the total cost function:

\[ c(x) = 5.50 + 20.50x \]

Thus, the correct answer is:

\[ \boxed{c(x) = 5.50 + 20.50x} \]