Question

write and solve the equation or inequality.

1. a dance instructor is deciding where to open her own studio. if the hairdresser chooses location a she will pay $1300 per month in rent and will charge $50 per haircut. if she choose location b, she will pay $1700 per month in rent and will charge $55 per haircut. how many haircuts would she have give to make the same profit at either location?

Explanation:

Step1: Define variable

Let \( x \) be the number of haircuts.

Step2: Profit for Location A

Profit = Revenue - Cost. Revenue for A: \( 50x \), Cost: \( 1300 \). So profit for A: \( 50x - 1300 \).

Step3: Profit for Location B

Revenue for B: \( 55x \), Cost: \( 1700 \). So profit for B: \( 55x - 1700 \).

Step4: Set profits equal

To find when profits are same, set \( 50x - 1300 = 55x - 1700 \).

Step5: Solve for \( x \)

Subtract \( 50x \) from both sides: \( -1300 = 5x - 1700 \).
Add \( 1700 \) to both sides: \( 400 = 5x \).
Divide by \( 5 \): \( x = 80 \).

Answer:

80