Question

A car rental company charges an initial fee plus a constant fee per kilometer driven.The table compares the total distance driven on the trip (in kilometers) and the price of the rental (indollars)Distance (kilometers)Price (dollars)105183140204175225What is the company's initial fee?

Answer 1

We have a linear relationship between the price of the rental and the distance driven.

We have to find the initial fee.

We can write the cost per distance x as:

$C(x)=b+mx$

where b is the initial fee, equal to the cost when the distance is x=0, and m is the variable fee per km.

If we find the slope of the line, then we can calculate the initial fee.

We pick the points (105,183) and (140,204) to calculate he slope as:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{204-183}{140-105}=\frac{21}{35}=0.6$

Then, using one ot the points, and replacing in the equation, we can find the value of b:

$\begin{gathered} y=0.6x+b \\ 204=0.6\cdot140+b \\ 204=84+b \\ b=204-84 \\ b=120 \end{gathered}$

The value of b, that represents the initial fee, is $120.

Answer: The initial fee is $120.