You are choosing between two health clubs.  Club A offers membership for a fee of $ 24 plus a monthly fee of $ 15.  Club B offers membership for a fee of $ 16 plus a monthly fee of $ 19.  After how many months will the total cost of each health club be the​ same?  What will be the total cost for each​ club?

To determine after how many months the total cost of each health club will be the same and what that total cost will be, we need to set up equations for the total cost of each club and find when these equations are equal.

Let's define the variables:

- Let $ x $ be the number of months.
- The total cost for Club A, $ C_A $, is given by the equation:
  \[
  C_A = 24 + 15x
  \]
- The total cost for Club B, $ C_B $, is given by the equation:
  \[
  C_B = 16 + 19x
  \]

We want to find the value of $ x $ for which $ C_A = C_B $.

### Step-by-Step Solution

1. **Set the equations equal to each other:**

\[
24 + 15x = 16 + 19x
\]

2. **Solve for $ x $:**

   - Subtract $ 15x $ from both sides:

\[
24 = 16 + 4x
\]

   - Subtract 16 from both sides:

\[
8 = 4x
\]

   - Divide both sides by 4:

\[
x = 2
\]

So, after 2 months, the total costs of both clubs will be the same.

3. **Calculate the total cost for each club when $ x = 2 $:**

   - For Club A:

\[
C_A = 24 + 15(2) = 24 + 30 = 54
\]

   - For Club B:

\[
C_B = 16 + 19(2) = 16 + 38 = 54
\]

### Conclusion

After 2 months, the total cost of each health club will be the same, which is **$54**.

---

Would you like more details or have any questions?

Here are 5 additional questions you might consider:

1. What is the cost difference between the two clubs after 1 month?
2. How much would you pay for each club after 6 months?
3. How do the initial fees impact the choice between the two clubs over a longer period?
4. If a third club offers a different pricing structure, how would you determine which club is cheapest over a certain period?
5. What is the maximum number of months after which Club A becomes cheaper than Club B?

**Tip:** When comparing costs over time, it’s helpful to set up equations and solve for the point where costs are equal, especially for services with different fixed and variable rates.

Discover how to compare health club memberships using mathematical equations. Learn when the total costs of two clubs, Club A and Club B, become equal based on their membership fees and monthly costs. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation