We can represent the total cost $C$ as a function of the number of classes $x$ attended as follows:

$C(x) = 50 + 10x$

• The term $50$ represents the fixed membership fee.
• The term $10x$ represents the cost for attending $x$ classes, where each class costs 10 dollars.

Now, to find the maximum number of classes you can attend given a budget of 200 dollars, we can set $C(x) \leq 200$ and solve for $x$:

$50 + 10x \leq 200$

Subtract 50 from both sides:

$10x \leq 150$

Now divide by 10:

$x \leq 15$

Thus, the maximum number of classes you can attend is 15.

Would you like further details or have any questions?

Here are 5 related questions:

1. How would the function change if the membership fee increased to $60?
2. What would the function look like if there was also a discount of $5 after attending 10 classes?
3. How would you solve for $x$ if your budget was $250?
4. What if the class price increased to $15 per class, how many classes could you afford?
5. What if the gym offered a one-time discount of $20, how many classes could you attend?

Tip: When working with linear functions, always identify fixed and variable components to set up your equation efficiently.