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 the equation for the total cost of 5 tickets: 5 p + 5.50 = 108.00 .
Solve for the price per ticket, p : p = 5 108.00 − 5.50 = 20.50 .
Formulate the linear function for the total cost c ( x ) : 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 are given that the total cost for ordering 5 tickets is $108.00 , which includes a fixed service fee of $5.50 . 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 can be expressed as: 5 p + 5.50 = 108.00
Calculating 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 .
Examples
Imagine you're planning a school trip to a museum. The museum charges a fixed booking fee plus a price per student. Knowing this linear relationship helps you calculate the total cost based on the number of students attending. For instance, if the booking fee is $5.50 and the price per student is $20.50 , you can easily determine the total cost for any number of students. This understanding allows for accurate budgeting and financial planning for the trip. Linear functions are essential for managing costs and making informed decisions in various real-life scenarios, from event planning to resource allocation.
The linear function representing the total cost when ordering x tickets is c ( x ) = 20.50 x + 5.50 . This is derived from the equation formed by considering the total cost for 5 tickets, which includes a fixed service fee. The correct multiple-choice option is A: c ( x ) = 5.50 + 20.50 x .
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