Please explain how to solve this equation with substitution: 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. How much does the owner charge for the haircut? Solve by writing and solving a system of equations.
o=A+21
6o+12A=750
put the first equation into the second.
6(A+21)=12A=750
now simplify, solve for A.
Then, O=A+21
To solve this equation using substitution, we need to set up a system of equations based on the given information and then solve it. Let's start by assigning variables to the unknowns.
Let's call the amount charged by the assistant for a haircut "A" in dollars, and the amount charged by the owner for a haircut "O" in dollars.
From the given information, we can set up the following equations:
Equation 1: "The owner charges $20 more per haircut than the assistant."
O = A + 20
Equation 2: "Yesterday the assistant gave 12 haircuts and the owner gave 6 haircuts. The total earnings from haircuts were $750."
12A + 6O = 750
Now that we have our system, we can use substitution to solve it. Let's substitute the value of O from Equation 1 into Equation 2:
12A + 6(A + 20) = 750
Simplify the equation by distributing:
12A + 6A + 120 = 750
Combine like terms:
18A + 120 = 750
Subtract 120 from both sides to isolate the term with A:
18A = 630
Divide both sides by 18 to solve for A:
A = 35
So the assistant charges $35 for a haircut.
Now that we have the value of A, we can substitute it back into Equation 1 to find the amount charged by the owner:
O = A + 20
O = 35 + 20
O = 55
Therefore, the owner charges $55 for a haircut.
To summarize:
The assistant charges $35 for a haircut, while the owner charges $55.