Chapter 3.9, Problem 3P

To determine

To Find: The charges charged by the plumber for eight-hours.

Answer to Problem 3P

The answer is $235.

Explanation of Solution

Given information: Given that the charges charged in different hours.

Calculation:

Let the x be the hours worked and $f(x)$ be the charges charged by plumber, we have $f(x)=ax+b$

First, we have to find a and b

  $\begin{array}{l}\text{Given}\text{that}\text{when}x=3,\text{we}\text{get}f(x)=110\\ \text{so,}\text{put}\text{this}\text{values}\text{on}\text{the}\text{above}\text{equation,}\text{we}\text{have}\\ 110=a\times 3+b\\ 110=3a+b\\ 3a+b=110\mathrm{...}(1)\\ \text{Similarly,}\text{when}\text{we}\text{put}x=5\text{and}f(x)=160,\text{we}\text{have}\\ 160=a\times 5+b\\ 160=5a+b\\ 5a+b=160\mathrm{...}(2)\\ \text{From}(1),\text{we}\text{get}\\ b=110-3a\\ \text{put}\text{this}\text{value}\text{on}(2),\text{we}\text{get}\\ 5a+110-3a=160\\ 2a=50\\ a=25\text{and}\\ b=110-3\times 25\\ b=110-75\\ b=35\end{array}$

Thus, the required linear function is $f(x)=25x+35$

Now, the charges for eight-hour job will be

  $\begin{array}{l}f(x)=25\times 8+35\\ f(x)=200+35\\ f(x)=235\end{array}$

Hence, the charge for eight-hour job is $235.