https://file.aiquickdraw.com/mathbot/file/1727199673673yw28i8tl.jpg

Let's work through the problem in three parts as requested in the image:

### Part A:
Kylie pays a yearly fee of $120 for membership, and each yoga lesson costs $5. If Kylie attends $ x $ yoga lessons, the total yearly cost $ C $ is made up of both the membership fee and the cost of the lessons. Therefore, the equation for the yearly cost is:

\[
C = 5x + 120
\]

Where:
- $ C $ is the total yearly cost,
- $ x $ is the number of yoga lessons attended,
- $5 is the cost per yoga lesson, and
- $120 is the yearly membership fee.

### Part B:
Now, Kylie spends a total of $160 for the year. To find out how many yoga lessons she attended, we substitute $ C = 160 $ into the equation from Part A and solve for $ x $:

\[
160 = 5x + 120
\]

Subtract 120 from both sides:

\[
160 - 120 = 5x
\]

\[
40 = 5x
\]

Now, divide by 5:

\[
x = \frac{40}{5} = 8
\]

So, Kylie attended **8 yoga classes**.

### Part C:
At the competing health club "Chiseled Angles," the membership is a one-time fee of $199.99, and members can attend unlimited yoga classes for the year.

For Kylie, the "Chiseled Angles" would be a better option if the total cost at her current club exceeds $199.99. Using the equation from Part A, we need to find when her cost exceeds $199.99:

\[
5x + 120 > 199.99
\]

Subtract 120 from both sides:

\[
5x > 79.99
\]

Now, divide by 5:

\[
x > \frac{79.99}{5} \approx 16
\]

Therefore, if Kylie plans to attend more than **16 yoga classes** in a year, it would be better for her to switch to "Chiseled Angles," because the total cost would be lower.

---

### Would you like further details or clarification on any of these steps?

### 5 related questions:
1. What would the cost be if Kylie attended 12 yoga classes?
2. If the yoga class cost increased to $6 per lesson, how would the equation in Part A change?
3. How would the breakeven point change if "Chiseled Angles" reduced their membership price to $180?
4. What if Kylie attended only 5 classes a year; which membership would be more economical?
5. How many yoga classes would Kylie need to attend for her total cost to exceed $250?

### Tip:
Whenever comparing two plans or options, always calculate the breakeven point, where the total costs are equal, to determine which is more cost-effective based on usage.

Yoga lessons cost $5 per lesson if Kylie enrolls in the health club for a fee of $120 per year. Write an equation that represents the yearly cost of yoga lessons. If Kylie spends a total of $160 for the year, how many yoga classes did she attend? A competing health club offers unlimited yoga for a one-time price of $199.99. When would this be a better choice for Kylie?

Learn how to solve cost comparison problems involving yoga lessons and health club memberships using linear equations. This problem covers key algebraic concepts such as solving linear equations and inequalities. Suitable for students in Grades 8-10.

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