Answer:Let's assume the number of haircuts Hayley needs to perform in a month for the total amount paid to either salon to be the same is denoted as 'x'.
For self-employment at The Princeton Salon:
Hayley would pay a fixed monthly rent of $774 to rent a station and keep all of her earnings.
For working at a franchise:
Hayley would have to pay $9 to the salon for every haircut she performs.
Based on the given information, we can set up the following equation to find the value of 'x':
Number of haircuts * Cost per haircut at franchise = Monthly rent at The Princeton Salon
x * 9 = 774
Solving for 'x':
x = 774/9
x ≈ 86.00
So, Hayley would need to perform approximately 86 haircuts in a month for the total amount paid to either salon to be the same.
Now, to calculate the total amount paid to either salon, we can use the following formulas:
Total amount paid at The Princeton Salon = Monthly rent + Earnings (which would be all of her earnings, as mentioned in the prompt)
Total amount paid at the franchise = Cost per haircut * Number of haircuts
Plugging in the values:
Total amount paid at The Princeton Salon = $774 + (Earnings from haircuts)
Total amount paid at the franchise = $9 * 86
Since the total amount paid to either salon is the same, we can equate the two equations:
$774 + Earnings from haircuts = $9 * 86
Solving for Earnings from haircuts:
Earnings from haircuts = $9 * 86 - $774
Earnings from haircuts = $774
So, Hayley would pay a total of $774 in earnings from haircuts, regardless of whether she chooses self-employment at The Princeton Salon or working at the franchise. The number of haircuts she needs to perform to reach this amount is 86.
Explanation: