https://file.aiquickdraw.com/mathbot/file/1726814476706x0uttv5a.jpg

Let's break down the problem step-by-step.

1. **Monthly Fee:** The problem states that the monthly fee is $50.
2. **Total Cost for 2 Months:** It mentions that the total cost for 2 months, including the joining fee, is $250.

We can set up an equation for the total cost, $ C $, for $ t $ months as:

\[
C = \text{Joining Fee} + (\text{Monthly Fee} \times t)
\]

### Determining the Joining Fee
Using the given information:
\[
250 = \text{Joining Fee} + (50 \times 2)
\]

\[
250 = \text{Joining Fee} + 100
\]

\[
\text{Joining Fee} = 250 - 100 = 150
\]

So, the joining fee is $150.

### General Equation
Now we can write the general equation for the total cost $ C $ for $ t $ months:

\[
C = 150 + 50t
\]

This equation represents the total cost of the gym membership over $ t $ months.

Would you like more details or have any questions?

Here are 5 related questions to explore:
1. What would the cost be after 6 months?
2. How would the equation change if the monthly fee increased?
3. What is the cost after 0 months, i.e., just the joining fee?
4. How much would Aubrey pay for 12 months?
5. What if the joining fee was waived?

**Tip:** Always isolate the unknown variable when forming an equation to ensure clarity in your solution.

Aubrey is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. The monthly fee to be a member is $50 and the total cost of membership, including the joining fee, would be $250 for 2 months. Write an equation for C, in terms of t, representing the total cost of the gym membership over t months.

Learn how to calculate the total cost of a gym membership, including a one-time joining fee and a monthly fee of $50. This problem involves setting up a linear equation in terms of t months. Suitable for students in Grades 6-8.

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