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

Explanation:

Step1: Find the cost per ticket

Let the price per ticket be \( p \). The total cost for 5 tickets is the cost of 5 tickets plus the service fee. So we have the equation \( 5p + 5.50 = 108.00 \). Subtract 5.50 from both sides: \( 5p = 108.00 - 5.50 = 102.50 \). Then divide by 5: \( p=\frac{102.50}{5} = 20.50 \).

Step2: Form the linear function

The total cost \( c(x) \) is the service fee plus the cost per ticket times the number of tickets. The service fee is 5.50 and the cost per ticket is 20.50. So \( c(x)=5.50 + 20.50x \).

Answer:

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