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 haircuts were $750. Hw much does the owner charge for a haircut? Solve by writing and solving a system of equations.
A = O - 20
6O + 12A = 750
6O + 12(O-20) = 750
Solve for O.
Thank you so much!:)
To solve this problem by writing and solving a system of equations, let's denote the cost of a haircut by the assistant as "x" dollars.
According to the given information, the owner charges $20 more per haircut than the assistant. Therefore, the cost of a haircut by the owner would be "x + $20" dollars.
Now, let's determine the total earnings from haircuts made by the assistant and the owner.
The assistant gave 12 haircuts, each costing "x" dollars, so the total earnings from haircuts by the assistant would be: 12x dollars.
The owner gave 6 haircuts, each costing "x + $20" dollars, so the total earnings from haircuts by the owner would be: 6(x + $20) dollars.
According to the problem, the total earnings from haircuts were $750. Therefore, we can set up the following equation:
12x + 6(x + $20) = $750
Now, let's solve this equation step by step:
First, distribute the 6 to (x + $20):
12x + 6x + 6($20) = $750
12x + 6x + $120 = $750
Next, combine like terms:
18x + $120 = $750
Now, isolate the variable by subtracting $120 from both sides of the equation:
18x = $750 - $120
18x = $630
Finally, solve for x by dividing both sides by 18:
x = $630 รท 18
x = $35
Therefore, the assistant charges $35 for a haircut.
To find out how much the owner charges for a haircut, we can substitute the value of x into the expression "x + $20":
$35 + $20 = $55
Thus, the owner charges $55 for a haircut.