The amount of money a state fair charges is modeled by the function [tex]f(x) = 1.75x + 12.50[/tex], where [tex]x[/tex] is the number of tickets a person purchases to ride the rides.

Calculate and interpret the real-world context of [tex]f(24)[/tex].

A. [tex]f(24) = 42[/tex]; A person who purchases 24 tickets will pay \$42.
B. [tex]f(24) = 6.57[/tex]; A person who purchases 24 tickets will pay \$6.57.
C. [tex]f(24) = 42[/tex]; A person who pays \$24 will have 42 tickets.
D. [tex]f(24) = 6.57[/tex]; A person who pays \$24 will have about 7 tickets.

Answer :

To solve this problem, we need to evaluate the function [tex]\( f(x) = 1.75x + 12.50 \)[/tex] at [tex]\( x = 24 \)[/tex].

Here's how to interpret and solve it step-by-step:

1. Understand the function: The function [tex]\( f(x) = 1.75x + 12.50 \)[/tex] represents the total cost in dollars for purchasing [tex]\( x \)[/tex] tickets at a state fair. Here, [tex]\( 1.75 \)[/tex] is the cost per ticket, and [tex]\( 12.50 \)[/tex] is an initial fee you pay regardless of the number of tickets.

2. Substitute [tex]\( x = 24 \)[/tex]: To find the total cost when someone buys 24 tickets, we substitute [tex]\( x = 24 \)[/tex] into the function.

3. Perform the calculation:
[tex]\[
f(24) = 1.75 \times 24 + 12.50
\][/tex]

4. Calculate the cost of the tickets:
[tex]\[
1.75 \times 24 = 42
\][/tex]

5. Add the initial fee:
[tex]\[
42 + 12.50 = 54.5
\][/tex]

So, the interpretation is: A person who purchases 24 tickets will pay \$54.50.