Two health clubs offer different pricing plans for their members. Both health clubs charge a one-time sign-up fee and a monthly membership fee. The equation y, equals, 59, x, plus, 50*y*=59*x*+50 represents what Health Club A charges. Health Club B charges a $45 sign-up fee and $29 per month. What costs more, and by how much?

The total cost for both health clubs can be calculated using their respective pricing plans.

### Health Club A:
The equation representing the cost is:
\[
y = 59x + 50
\]
where:
- $x$ is the number of months.
- The one-time sign-up fee is $50.
- The monthly fee is $59.

### Health Club B:
The cost equation for Health Club B can be written as:
\[
y = 29x + 45
\]
where:
- $x$ is the number of months.
- The one-time sign-up fee is $45.
- The monthly fee is $29.

To compare the costs, we need to calculate the difference in costs between Health Club A and Health Club B for any given number of months $x$. The difference is given by subtracting the equation for Health Club B from that of Health Club A:
\[
\text{Difference} = (59x + 50) - (29x + 45)
\]
Simplifying this:
\[
\text{Difference} = 59x + 50 - 29x - 45 = 30x + 5
\]
This equation shows that Health Club A costs $(30x + 5)$ dollars more than Health Club B after $x$ months.

- For $x = 1$ month, the difference is $30(1) + 5 = 35$ dollars.
- For $x = 6$ months, the difference is $30(6) + 5 = 185$ dollars.

Thus, **Health Club A costs more by $30x + 5$ dollars** for any number of months $x$. If you'd like, we can calculate the cost for a specific number of months.

---

Do you want more details or have any questions?

Here are 5 related questions:
1. How would the costs change for a year-long membership?
2. What happens if Health Club B increases its sign-up fee?
3. How many months would it take for Health Club A to cost $100 more than Health Club B?
4. What if Health Club A had a monthly discount after 6 months?
5. Can the difference between the two clubs' costs ever be negative?

**Tip:** When comparing similar services, look for a break-even point where one option becomes more affordable.

Two health clubs offer different pricing plans for their members. Both health clubs charge a one-time sign-up fee and a monthly membership fee. The equation y = 59x + 50 represents what Health Club A charges. Health Club B charges a $45 sign-up fee and $29 per month. What costs more, and by how much?

This problem compares the costs of two health clubs using linear equations. Health Club A charges a $50 sign-up fee and $59 per month, while Health Club B charges $45 for sign-up and $29 per month. Learn how to use algebra to find which club costs more and by how much. Suitable for students in Grades 6-8.

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