Question

#4. For a performance of King Lear, student tickets cost $18 and adult tickets cost $28. In all, 320 people attended the performance and ticket receipts totaled $8060. How many tickets of each type were sold?

Answer 1

Let the number of student tickets and adult tickets sold be x and y respectively. Since 320 people attended the performance, therefore x+y = 320….(1). Further, since student tickets cost $18, adult tickets cost $28 and since the ticket receipts totaled $8060, therefore 18x+28y = 8060 or, on dividing both the sides by 2, we get 9x+14y = 4030…(2).

On multiplying the 1^stequation by 9 and on subtracting the result from the 2^nd equation, we get (9x+14y ) -(9x+9y) = 4030-2880 or, 5y = 1150 so that y = 1150/5 = 230. Now, on substituting y = 230 in the 1^st equation, we get x+230 = 320 so that x = 320-230 = 90. Thus, 90 student tickets and 230 adult tickets were sold.