Question

Solve the problem.

Two plumbers make house calls. One charges $105 for a visit plus $30 per hour of work. The other charges
$80 per visit plus $40 per hour of work. For how many hours of work do the two plumbers charge the same?

Answer 1

The two plumbers charge the same for 2.5 hours of work.

The first plumber's charge is given by F(x).

The second plumber's charge is given by S(x).

One charges $105 for a visit plus $30 per hour of work.

This means that, for x hours of work, the charge is given by:

The other charges $80 per visit plus $40 per hour of work.

This means that, for x hours of work, the charge is given by:

For how many hours of work do the two plumbers charge the same?

This is x for which:

So

The two plumbers charge the same for 2.5 hours of work.

Answer 2

The two plumbers charge the same for 2.5 hours of work.

Explanation:

The first plumber's charge is given by F(x).

The second plumber's charge is given by S(x).

One charges $105 for a visit plus $30 per hour of work.

This means that, for x hours of work, the charge is given by:

`F(x) = 105 + 30x`

The other charges $80 per visit plus $40 per hour of work.

This means that, for x hours of work, the charge is given by:

`S(x) = 80 + 40x`

For how many hours of work do the two plumbers charge the same?

This is x for which:

`S(x) = F(x)`

So

`80 + 40x = 105 + 30x`

`10x = 25`

`x = (25)/(10)`

`x = 2.5`

The two plumbers charge the same for 2.5 hours of work.