The Correct Answer and Explanation is:
Equation: 3.75x + 119 = 400.25
Answer: x = 75
Explanation
To solve this problem, we first need to construct a linear equation that represents the total cost of the computer repair. The problem gives us all the necessary components to build this equation. The total cost is comprised of two main parts: the fixed cost for the parts and the variable cost for the labor.
First, let’s identify the known values. The total bill Lauren paid was $400.25. The cost for the parts was a flat fee of $119. The technician worked for 3.75 hours. The unknown value we need to find is the cost of labor per hour, which the problem defines as x.
The total cost of labor can be calculated by multiplying the number of hours worked by the hourly labor rate. In this case, that is 3.75 hours multiplied by x dollars per hour, which can be written as the term 3.75x.
Now, we can set up the equation. The total cost is the sum of the labor cost and the parts cost. This gives us the following relationship:
(Total Labor Cost) + (Cost of Parts) = Total Bill
3.75x + 119 = 400.25
With the equation established, the next step is to solve for x. Our goal is to isolate the variable x on one side of the equation. We begin by subtracting the cost of the parts, $119, from both sides of the equation to maintain balance.
3.75x + 119 – 119 = 400.25 – 119
3.75x = 281.25
This new equation tells us that the total cost for the 3.75 hours of labor was $281.25. To find the cost for a single hour, we divide both sides of the equation by the number of hours, 3.75.
x = 281.25 / 3.75
x = 75
Therefore, the cost of the labor per hour is $75.
