Question

A plumber charges $65 for a consultation fee and x dollars for labor per hour.
Write an equation that would represent this situation if it took the plumber 5 hours to fix
a problem and the total cost is $240.
Find the plumber's hourly charge for labor.

a) 5x+$65=$240; x=$35
b) 5x-$65=$240; x=$61
c) $65-5x=$240; x=-$35
d) 5x+$240=$65; x=$45

Answer 1

To develop an equation to represent the situation, we begin with the total cost, which includes the consultation fee and the labor charge for the number of hours worked.

The plumber charges a consultation fee of $65 and an additional charge of \(x\) dollars for each hour of labor. If the plumber worked for 5 hours, the total labor cost would be \(5x\).

Thus, the total cost can be represented by the equation:

\[
5x + 65 = 240
\]

Now, to solve for \(x\), we can isolate \(x\) in the equation:

1. Subtract 65 from both sides:

\[
5x = 240 - 65
\]
\[
5x = 175
\]

2. Divide both sides by 5:

\[
x = \frac{175}{5}
\]
\[
x = 35
\]

So, the plumber's hourly charge for labor is \(x = 35\).

The correct option from the given choices is:

**a) 5x + 65 = 240; x = 35**.