An electrician charges $60 as a one-time fee plus an additional $55 per hour. If the total bill is $252.50, how many hours did it take for the electrician to complete the repair?

Question

Solve the equation using inverse operations. Show ALL work.

Answer 1

To find out how many hours it took for the electrician to complete the repair, we can set up an equation based on the information given:

Let \( h \) be the number of hours worked by the electrician.

The total cost for the service consists of a one-time fee plus the hourly charges: \[ \text{Total cost} = \text{One-time fee} + (\text{Hourly rate} \times h) \] Given that the one-time fee is $60 and the hourly rate is $55, we can express this as: \[ 252.50 = 60 + 55h \]

Now, we will solve for \( h \) using inverse operations step by step.

1. Subtract the one-time fee from both sides: \[ 252.50 - 60 = 55h \] \[ 192.50 = 55h \]

2. Now, divide both sides by 55 to solve for \( h \): \[ h = \frac{192.50}{55} \]

3. Calculating the division: \[ h = 3.5 \]

Thus, the number of hours it took for the electrician to complete the repair is \( \boxed{3.5} \) hours.

To verify the solution, we can plug \( h = 3.5 \) back into the original cost equation: \[ \text{Total cost} = 60 + 55(3.5) = 60 + 192.50 = 252.50 \]

Since the total calculated matches the given total bill, our solution is confirmed.