Question

Taxi fare in a city is rs. 8.00 for first kilometer and for the subsequent distance it is rs 5.00 per km. Write a linear equation to represent this information in two variables taking distance covered as 'x' km and total fare as 'y'. What will be the distance travelled by a person if he spent rs 63.00?

y=3x+5 , 12 km

y=5x+3, 12 km

x=5x+3, km18

y=5x+3, km 325​

Answer 1

x 0  1 2

y 3 8  13  

Taxi fare for first kilometer = Rs. 8

Taxi fare for subsequent distance = Rs. 5

Total distance covered =x

Total fare =y

Since the fare for first kilometer = Rs.8

According to problem,

Fare for (x–1) kilometer = 5(x−1)

So, the total fare y=5(x−1)+8

⇒y=5(x−1)+8

⇒y=5x–5+8

⇒y=5x+3

Hence, y=5x+3 is the required linear equation.

Now the equation is

y=5x+3    ...(1)

Now, putting the value x=0 in (1)

y=5×0+3

y=0+3=3 So the solution is (0,3)

Putting the value x=1 in (1)

y=5×1+3

y=5+3=8. So the solution is (1,8)

Putting the value x=2 in (1)

y=5×2+3

y=10+3=13. So the solution is (2,13)