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Andres needed to get his computer fixed. He took it to the repair store. The technician at the store worked on the computer for 5.25 hours and charged him [tex]$\$[/tex]116[tex]$ for parts. The total was $[/tex]\[tex]$719.75$[/tex].

Which equation could be used to determine [tex]\(c\)[/tex], the cost of labor per hour?

A. [tex]\(116 + 5.25c = 719.75\)[/tex]

B. [tex]\(116c + 5.25 = 719.75\)[/tex]

C. [tex]\(116c = 719.75 - 5.25\)[/tex]

D. [tex]\(c = \frac{116 - 719.75}{5.25}\)[/tex]


Sagot :

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].