7 answers
Part A:
Let \( h \) represent the number of hours the electrician worked.
Now the total cost can be expressed with the following equation based on the given charges:
Total bill = One-time fee + (Hourly rate × Number of hours) \[ \text{Total bill} = 60 + 55h \]
In this problem, the total bill is $252.50, so we can write the equation as: \[ 252.50 = 60 + 55h \]
Thus, the variable defined for this problem is \( h \), the number of hours worked by the electrician.
Part B:
Based on the situation described, the equation that represents the total bill for the electrician's services can be written as:
\[ 252.50 = 60 + 55h \]
In this equation:
Part C:
To solve the equation \( 252.50 = 60 + 55h \) using inverse operations, we will isolate the variable \( h \). Here are the steps:
Subtract 60 from both sides of the equation to eliminate the one-time fee:
\[ 252.50 - 60 = 55h \]
Simplifying the left side:
\[ 192.50 = 55h \]
Divide both sides by 55 to solve for \( h \):
\[ h = \frac{192.50}{55} \]
Now, performing the division:
\[ h = 3.5 \]
So, the solution is:
\[ h = 3.5 \]
This means it took the electrician 3.5 hours to complete the repair.
Part D:
The electrician worked for 3.5 hours, starting at 10:30 a.m. To determine what time he finished, we can break it down into two parts: 3 hours and 30 minutes.
Adding 3 hours to 10:30 a.m.:
\[ 10:30 , \text{a.m.} + 3 , \text{hours} = 1:30 , \text{p.m.} \]
Adding 30 minutes to 1:30 p.m.:
\[ 1:30 , \text{p.m.} + 30 , \text{minutes} = 2:00 , \text{p.m.} \]
So, the electrician finished with the repair at 2:00 p.m.
