Question

The taxi fare in a city is as follows. For the first kilometer, the fare is Rs.8 and for the subsequent distance it is Rs.5 per km, taking the distance covered as x km and total fare as Rs.y write a linear equation for this information.

Answer 1

Hint: In this question, we are given a taxi fare in a city. We need to form a linear equation using two variables x and y according to the given information. We will first find one kilometer and then for the rest of the journey. Adding them both, we will equate it to total fare as Rs.y. This will give us our required linear equation.

Complete step by step answer:
Here according to the question, taxi fare for one kilometer is Rs.8 and for the subsequent distance, it is Rs.5 per km. The total distance covered is given as x km. Now we know that, for the first kilometer, the fare is Rs.8, so our remaining distance will be (x-1)km for which fare is Rs.5 per km.

Fair of each kilometer after the first kilometer is Rs.5.
So fare for (x-1)km after the first kilometer will be Rs.5(x-1).
Now we are given a total fare Rs.y
Therefore, y is the sum of Rs.8 and Rs.5(x-1).
In mathematical form, we can write it as $y=8+5\left( x-1 \right)$.
Simplifying we get $y=8+5x-5\Rightarrow y=5x+3$.
Which is our required answer.
Note:
Students should note that, by putting x = 1, we get y = 8 which is the fare for 1 kilometer as given. For x = 2, we observe that y = 13, for x = 3, y = 18, for x = 4, y = 23. We can see, 8, 13, 18, 23, . . . . . . . is in arithmetic progression. Putting any number of kilometers, we can calculate the fare.