An electrician charges a customer $260 for 4 hours. He charges one customer $150 for 2 hours. How much does he charge for his service fee, x, and his hourly charge, y, to his customers?
Thank you!
x + 2y = 150
x + 4y = 260
solve the system
To find the service fee, x, and the hourly charge, y, of the electrician, we can set up a system of equations based on the given information.
Let's assume that the service fee is x and the hourly charge is y.
From the first statement, we know that the electrician charged $260 for 4 hours. This can be expressed as:
4y + x = 260 ----(1)
From the second statement, we know that the electrician charged $150 for 2 hours. This can be expressed as:
2y + x = 150 ----(2)
Now, we need to solve this system of equations. There are multiple ways to solve it, but one common method is substitution.
Solve equation (2) for x:
x = 150 - 2y
Substitute this value of x into equation (1):
4y + (150 - 2y) = 260
Simplify:
4y + 150 - 2y = 260
Combine like terms:
2y + 150 = 260
Subtract 150 from both sides:
2y = 110
Divide both sides by 2:
y = 55
Now, substitute y = 55 back into either equation (1) or (2) to find the value of x.
Using equation (1):
4(55) + x = 260
220 + x = 260
Subtract 220 from both sides:
x = 40
Therefore, the electrician charges a service fee of $40 and an hourly rate of $55.