Let's solve the problem step-by-step.
1. Identify the Known Values:
- The technician worked for a total of 5.25 hours.
- The cost of the parts used is [tex]$116.
- The total cost for fixing the computer is $[/tex]719.75.
2. Set Up the Equation:
We need to find the cost per hour of labor, denoted as [tex]\(c\)[/tex]. The total cost is made up of the cost of parts plus the cost of labor. Therefore, the equation can be written as:
[tex]\[
\text{Parts Cost} + (\text{Hours Worked} \times \text{Cost Per Hour}) = \text{Total Cost}
\][/tex]
Substituting the known values:
[tex]\[
116 + 5.25c = 719.75
\][/tex]
3. Solve for [tex]\(c\)[/tex]:
Isolate [tex]\(c\)[/tex] on one side of the equation:
[tex]\[
5.25c = 719.75 - 116
\][/tex]
Simplify the right-hand side:
[tex]\[
5.25c = 603.75
\][/tex]
4. Divide Both Sides by 5.25:
[tex]\[
c = \frac{603.75}{5.25}
\][/tex]
5. Calculate the Result:
After performing the division:
[tex]\[
c = 115.0
\][/tex]
The equation used to determine [tex]\(c\)[/tex], the cost of labor per hour, is:
[tex]\[
116 + 5.25c = 719.75
\][/tex]
And the cost of labor per hour is [tex]\( \$115.0 \)[/tex].
