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).
A. $c(x)=5.50+20.50 x$
B. $c(x)=5.50 x+20.50$
C. $c(x)=5.50+21.60 x$
D. $c(x)=5.50 x+21.60
Answer (2)
Set up an equation to represent the total cost for 5 tickets: 5 p + 5.50 = 108.00 , where p is the price per ticket.
Solve for p : p = 5 108.00 − 5.50 = 20.50 .
Formulate the linear function for the total cost c ( x ) for x tickets: c ( x ) = 20.50 x + 5.50 .
The linear function representing the total cost is c ( x ) = 5.50 + 20.50 x .
Explanation
Problem Analysis Let's analyze the problem. We know that the total cost for ordering tickets online consists of a fixed service fee and a price per ticket. We are given that the service fee is $5.50 and the total cost for 5 tickets is $108.00 . We need to find a linear function that represents the total cost c when x tickets are ordered.
Setting up the Equation Let p be the price per ticket. The total cost for 5 tickets is the sum of the cost of the 5 tickets and the service fee. So, we can write the equation: 5 p + 5.50 = 108.00
Solving for the Price per Ticket Now, we solve for p :
5 p = 108.00 − 5.50 5 p = 102.50 p = 5 102.50 p = 20.50 So, the price per ticket is $20.50 .
Finding the Linear Function The linear function representing the total cost c ( x ) for x tickets is given by: c ( x ) = p x + 5.50 Substituting the value of p we found: c ( x ) = 20.50 x + 5.50
Final Answer Therefore, the linear function that represents the total cost c when x tickets are ordered is: c ( x ) = 20.50 x + 5.50 This matches option c ( x ) = 5.50 + 20.50 x if we rewrite it.
Examples
Imagine you're planning a school trip to a museum. The museum charges $10 per student plus a flat booking fee of $25 . If you want to calculate the total cost for any number of students, you can use a linear function similar to the one in this problem. For example, if 30 students are going, the total cost would be c ( 30 ) = 10 × 30 + 25 = 325 , so the total cost is $325 . This type of calculation is useful for budgeting and planning any event with a fixed fee and a per-person cost.
The linear function representing the total cost of ordering tickets is c ( x ) = 5.50 + 20.50 x , where 5.50 is the service fee and 20.50 is the price per ticket. Therefore, option A is the correct choice. This function allows for calculating total costs based on the number of tickets ordered.
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