The owner of a hair salon charges $20 more per haircut than the assistant. Yesterday the assistant gave 12 haircuts. The owner gave 6 haircuts. The total earnings from the haircuts were $750. How much does the owner charge for a haircut? Solve by writing and solving a system of equations?
X: $55
Let the owner's charge be $x
then the assistant's charge is x-20
6x + 12(x-20) = 750
6x + 12x - 240 = 750
18x = 990
x = 55
To solve this problem using a system of equations, let's denote the price charged by the assistant as "x" dollars per haircut. Therefore, the price charged by the owner would be "x + 20" dollars per haircut.
Now, let's set up the system of equations based on the given information:
1) The assistant gave 12 haircuts, so the total earnings from the assistant's haircuts would be 12x dollars.
2) The owner gave 6 haircuts, so the total earnings from the owner's haircuts would be 6(x + 20) dollars.
We also know that the total earnings from all the haircuts were $750. Therefore, we can set up another equation:
3) 12x + 6(x + 20) = 750
Now, let's solve the system of equations:
Expanding the equation (3):
12x + 6x + 120 = 750
18x + 120 = 750
Moving 120 to the other side:
18x = 750 - 120
18x = 630
Dividing both sides by 18:
x = 630 / 18
x = 35
Therefore, the assistant charges $35 per haircut. Since the owner charges $20 more than the assistant, the owner charges $35 + $20 = $55 per haircut.