Question

The auto fares in a city are as follows:
For the first kilometer, the fare is Rs. 8 and for the subsequent distance it is Rs. 3.5 per km. Taking the distance covered as ‘x’ km and total fare Rs. y, write a linear equation for the information.

Answer 1

Hint: To find the total auto fare of the city, equate the variable representing total fare with the sum of fare for first kilometer and total fare for the remaining distance. Now, to find the fare for distance covered after one km, multiply the total distance covered with the fare for each kilometer.

Complete step-by-step solution -
Let us come to the question. We have been given that, for the first kilometer, the fare is Rs. 8 and for the subsequent distance it is Rs. 3.5 per km. Also, it is said that we have to consider the total distance covered as ‘x’ km and total fare is Rs. y. Therefore,
$\text{Total fare}=\text{fare for first km}+\text{remaining distance travelled}\times \text{fare for each km}$
Now, after travelling one km, the total distance left to travel = (x-1) km.
Therefore, total fare for (x-1) km $=(x-1)\times 3.5=3.5x-3.5$.
Therefore, total fare is given as,
$\begin{align}
  & y=8+3.5x-3.5 \\
 & \Rightarrow y=3.5x+4.5 \\
\end{align}$
Hence, the total auto fare of the city in the form of a linear equation is, $y=3.5x+4.5$.

Note: Here one important thing you can note is that we are not asked to solve the obtained equation because there is not sufficient information so that we can solve this equation. It is said to us that we have to form the equation only. So don’t get confused and don’t try to solve the equation.