The Correct Answer and Explanation is:
Equation: 3.75x + 119 = 400.25
Answer: x = 75
Explanation
To solve this problem, we first need to understand the components that make up the total cost of the computer repair. The total cost is a combination of a fixed cost for the parts and a variable cost for the labor. The problem provides us with the total cost, the cost of the parts, and the number of hours the technician worked. Our goal is to find the cost of labor per hour, which is represented by the variable x.
The equation is built by setting the sum of the parts and labor costs equal to the total bill.
- Cost of Parts: This is a fixed amount given as $119.
- Cost of Labor: This is calculated by multiplying the number of hours the technician worked by the hourly rate (x). The technician worked for 3.75 hours, so the total labor cost is 3.75 times x, or 3.75x.
- Total Cost: The final bill was $400.25.
By adding the cost of parts and the cost of labor, we get the total cost. This gives us the equation: 3.75x + 119 = 400.25.
To solve for x, we need to isolate the variable. First, we subtract the cost of the parts from both sides of the equation to determine the total amount charged for labor.
3.75x + 119 – 119 = 400.25 – 119
3.75x = 281.25
Now we know that the total labor cost was $281.25. To find the hourly rate (x), we divide this total labor cost by the number of hours worked, which is 3.75.
3.75x / 3.75 = 281.25 / 3.75
x = 75
Therefore, the cost of the labor per hour is $75.
