MATHEMATICS · Multi-part · A Level · Mathematics · Algebra and Functions · Algebra and Functions
Problem
At a school fair, a stall sells two kinds of coupons: ‘Fun’ coupons for adults and ‘Joy’ coupons for children. One customer buys 4 Fun coupons and 6 Joy coupons for ₹460, while another customer buys 6 Fun coupons and 4 Joy coupons for ₹500.
(i) Form a pair of linear equations in two variables representing the above information, taking the cost of one Fun coupon as ₹x and one Joy coupon as ₹y.
(ii) Without actually solving the equations, determine whether the pair of equations has a unique solution, no solution, or infinitely many solutions. State your reason clearly.
(iii) Solve the equations obtained in part (i) and hence find the cost of one Fun coupon and one Joy coupon.