A cinema hall charges two different ticket rates for adults and students
MATHEMATICS · Multi-part · AoPS · Mathematics · Multi-Variable Linear Equations · Multi-Variable Linear Equations
Problem
A cinema hall charges two different ticket rates for adults and students. On a certain day:
• 7 adult tickets and 5 student tickets together cost ₹2,560.
• 4 adult tickets and 9 student tickets together cost ₹2,340.
(i) Let the price of an adult ticket be ₹x and that of a student ticket be ₹y. Frame the pair of linear equations based on the given data.
(ii) Solve the equations obtained in part (i) to find the individual ticket prices.
(iii) Verify your answers by substituting the calculated prices back into both original cost conditions.
(iv) Using the prices obtained, determine the total collection if 120 adult tickets and 180 student tickets are sold for the evening show.