Question

The manager at a concert venue keeps track of the number of adult tickets and student tickets sold each day and the total money received. On Wednesday, a total of 74 tickets were sold, and the money collected was $994. If adult tickets are sold for $15 and student tickets are sold for $11, how many adult tickets and student tickets were sold? Give your answer as an ordered pair (x,y), where x is the number of adult tickets and y is the number of student tickets.

Answer 1

Answer: the number of adult and student tickets sold are (45, 29)

Step-by-step explanation:

Let x represent the number of adult tickets that were sold.

Let y represent the number of student tickets that were sold.

On Wednesday, a total of 74 tickets were sold. This means that

x + y = 74

x = 74 - y- - - - - - - - - - - - - - 1

If adult tickets are sold for $15 and student tickets are sold for $11 and the money collected was $994, it means that

15x + 11y = 994- - - - - - - - - - - - - - 2

Substituting equation 1 into equation 2, it becomes

15(74 - y) + 11y = 994

1110 - 15y + 11y = 994

- 15y + 11y = 994 - 1110

- 4y = - 116

y = - 116/ - 4

y = 29

Substituting y = 29 into equation 1, it becomes

x = 74 - 29 = 45