Chapter 3.9, Problem 5P

To determine

To Find: The cost of a trip for a distance of 1000 miles.

Answer to Problem 5P

The answer is $315.

Explanation of Solution

Given information: Given that the fare charges of a ticket for different distances.

Calculation:

Let x be the total distance travelled and $f(x)$ be the fair charges of that distance than, we have $f(x)=ax+b$

First, we have to find a and b

  $\begin{array}{l}\text{Given}\text{that}\text{when}x=260,\text{we}\text{get}f(x)=90\\ \text{so,}\text{put}\text{this}\text{values}\text{on}\text{the}\text{above}\text{equation,}\text{we}\text{have}\\ 900=a\times 260+b\\ 90=260a+b\\ 260a+b=90\mathrm{...}(1)\\ \text{Similarly,}\text{when}\text{we}\text{put}x=500\text{and}f(x)=150,\text{we}\text{have}\\ 150=a\times 500+b\\ 150=500a+b\\ 500a+b=150\mathrm{...}(2)\\ \text{From}(1),\text{we}\text{get}\\ b=90-260a\\ \text{put}\text{this}\text{value}\text{on}(2),\text{we}\text{get}\\ 500a+90-260a=150\\ 240a=60\\ a=\frac{60}{240}=0.25\text{and}\\ b=90-260\times 0.25\\ b=90-65\\ b=25\end{array}$

Thus, the required linear function is $f(x)=0.25x+65$

Now, the cost of trip for 1000 miles will be

  $\begin{array}{l}f(x)=0.25\times 1000+65\\ f(x)=250+65\\ f(x)=315\end{array}$

Hence, the cost of trip for 1000 miles is $315.