MATHEMATICS · Multi-part · AoPS · Mathematics · Multi-Variable Linear Equations · Multi-Variable Linear Equations
Problem
During a school fete, adult tickets were sold for ₹50 each and child tickets for ₹30 each. On a particular day, 120 tickets were sold and the total collection was ₹4,200.
(i) If x adult tickets and y child tickets were sold, write two linear equations representing the given information.
(ii) Choose two convenient ordered pairs for each equation and plot the corresponding lines on a graph, labelling all axes and scales clearly.
(iii) Obtain the exact number of adult and child tickets sold that day from the point of intersection of the two lines.
(iv) On the next day, 150 tickets were sold in all, with the number of child tickets exceeding the number of adult tickets by 30. Using the graphical method on the same set of axes (draw any additional line required), determine how many tickets of each type were sold on the second day.