The amount of money a gym charges for a monthly membership is modeled by the function [tex]f(x) = 15x + 200[/tex], where [tex]x[/tex] is the number of spin classes a person attends. Calculate and interpret the real-world context of [tex]f(10)[/tex].

A. [tex]f(10) = 225[/tex]; A person who attends 10 spin classes will pay \$225.

B. [tex]f(10) = 350[/tex]; A person who attends 10 spin classes will pay \$350.

C. [tex]f(10) = 215[/tex]; A person who pays \$215 will attend 10 spin classes.

D. [tex]f(10) = 150[/tex]; A person who pays \$150 will attend 10 spin classes.

To solve the problem of finding the amount a gym charges based on the number of spin classes attended, we start by using the function given:

[tex]\[ f(x) = 15x + 200 \][/tex]

This function describes the total monthly membership cost as a combination of a base fee and an additional cost per spin class. In this formula:

- [tex]$ x $[/tex] represents the number of spin classes attended.
- The term [tex]$ 15x $[/tex] accounts for the cost related to spin classes, where each class costs [tex]$15.
- The constant 200 represents a fixed base fee for the monthly membership.

We need to calculate the total cost for someone who attends 10 spin classes. To find this, we substitute $ x = 10 $ into the function:

\[ f(10) = 15 \times 10 + 200 \]

This simplifies to:

\[ f(10) = 150 + 200 \]

\[ f(10) = 350 \]

So, the interpretation of $ f(10) = 350 $ in the real-world context is:

"A person who attends 10 spin classes will pay $[/tex]350."

This means that the total monthly cost for membership, considering attending 10 spin classes, amounts to $350.