Rita is looking for a job cutting hair. One option is self-employment at The Arcadia Salon, where she would pay $444 per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon $2 for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How many haircuts would that be? How much would Rita pay?

Let's define the number of haircuts Rita performs in a month as $ x $.

### Option 1: Self-Employment at The Arcadia Salon
- Rita pays a fixed rent of \$444 per month.

### Option 2: Working at a Franchise
- Rita pays \$2 per haircut, so her total payment is $ 2x $.

We are looking for the number of haircuts $ x $ such that the amount paid to either salon is the same.

### Setting up the equation:
\[
444 = 2x
\]
Now, solve for $ x $:
\[
x = \frac{444}{2} = 222
\]

So, the number of haircuts is **222**.

### How much would Rita pay?
Since Rita would perform 222 haircuts, the amount she pays is:
\[
2 \times 222 = 444 \text{ dollars}
\]

Thus, Rita would pay **\$444** in both cases if she performs 222 haircuts.

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Would you like more details or have any questions?  
Here are some related questions to consider:

1. What if the franchise charged \$3 per haircut instead of \$2?
2. How much would Rita earn after paying the franchise per haircut?
3. What if Rita wants to break even with fewer haircuts? How would the rent at Arcadia change?
4. How does this comparison change if Rita's income per haircut varies?
5. How many haircuts would Rita need to profit in each scenario?

**Tip:** When comparing flat fees with per-unit costs, set up an equation and solve for the breakeven point.

Explore how to compare fixed rent at Arcadia Salon and per-haircut franchise fees using algebraic linear equations. This example shows how Rita can calculate when she would pay the same amount at both salons and includes a step-by-step breakdown suitable for students in Grades 6-8.

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