If a local gym charges a membership fee of 50$ plus an additional 10$ per class attended, how can we represent the total cost C as a function of the number classes x attended?

what is the maximum number of classes you could attend in a month if your budget is 200$

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.

If a local gym charges a membership fee of 50$ plus an additional 10$ per class attended, how can we represent the total cost C as a function of the number of classes x attended? What is the maximum number of classes you could attend in a month if your budget is 200$?

Learn how to calculate the total cost of a gym membership with a fixed fee and per-class charge. This example uses linear equations to find the maximum number of classes you can attend on a $200 budget. Ideal for students in Grades 6-8.

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