Solve the Problem $\$ 60$ Per Ticket, That Is, the Cost Function Is

question 378

Multiple Choice

Solve the problem.
-The cost to buy tickets online for a dance show is $\$ 60$ per ticket, that is, the cost function is $C ( x ) =$ $60 x$ for $x$ tickets to the show. There is a sales tax of $4.5 \%$ and a processing fee of $\$ 7$ for a group of tickets, that is, $T ( x ) = 1.045 x + 7$ is the total cost for $x$ dollars spent on tickets.
(a) Find $( T \circ C ) ( x )$
(b) Find $( T \circ C ) ( 7 )$ and interpret its meaning in the context of the problem.

• A) (a) \(( T \circ C ) ( x ) = 62.7 x + 7\); (b) \(( T \circ C ) ( 7 ) = 445.9\); The total cost to purchase 7 tickets.
• B) (a) \(( T \circ C ) ( x ) = 62.7 x + 7\); (b) \(( T \circ C ) ( 7 ) = 445.9\); The average cost per ticket.
• C) (a) \(( T \circ C ) ( x ) = 62.7 x + 420\); (b) \(( T \circ C ) ( 7 ) = 858.9\); The total cost to purchase 7 tickets.
• D) (a) \(( T \circ C ) ( x ) = 62.7 x + 420\); (b) \(( T \circ C ) ( 7 ) = 858.9\); The average cost per ticket.

---

Definitions:

Aristotle

An ancient Greek philosopher and polymath whose extensive writings cover a wide range of subjects, including physics, metaphysics, logic, ethics, and politics, significantly influencing Western intellectual history.

Personality

The combination of characteristics or qualities that form an individual's distinctive character, influencing thoughts, motivations, and behaviors.

Scientific Attitude

A mindset characterized by curiosity, skepticism, and openness to empirical evidence and logical arguments when evaluating claims or hypotheses.

Curiosity

A strong desire to know or learn something, driving individuals to explore, investigate, and seek out new information or experiences.