Two courier companies A and B charge customers according to the distance kilometres…
MATHEMATICS · Multi-part · CBSE · Mathematics · Pair of Linear Equations in Two Variables · Pair of Linear Equations in Two Variables
Problem
Two courier companies A and B charge customers according to the distance x kilometres that a parcel has to be delivered. Company A charges a fixed handling fee of ₹50 plus ₹12 per kilometre, while company B charges a fixed handling fee of ₹70 plus ₹10 per kilometre. Let the total cost in rupees be y for each company.
(i) Write one linear equation in the variables x and y for each company in the general form ax+by+c=0.
(ii) Draw the graphs of both equations on the same Cartesian plane, choosing suitable scales.
(iii) From the point of intersection of the two graphs, determine the distance at which both companies charge the same amount and state that common cost.
(iv) Comment on the nature of the solution set represented by the two equations, explaining how your graphical work supports your answer.