Two taxi companies in a town charge according to the distance travelled

MATHEMATICS · Multi-part · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables

Problem

Two taxi companies in a town charge according to the distance travelled. For Company A, the cost (in rupees) is given by

6x+50

, and for Company B the cost (in rupees) is given by

8x+30

, where

x

is the distance in kilometres. (a) Write the two linear equations in the variables

x

and

y

, where

y

represents the total fare in rupees for each company. (b) Draw the graphs of both equations on the same axes, taking

1\,\text{cm}=1\,\text{km}

on the

x

-axis and

1\,\text{cm}=10

rupees on the

y

-axis. (c) From your graph find the distance for which both companies charge the same fare and state this common fare. (d) Interpret your answer of part (c) in the context of the problem. (e) Confirm the values obtained in part (c) by solving the pair of equations algebraically.

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