The managed of a movie theater found that saturday's sales were $3657. He knew that a total of 650 tickets were sold saturday. Adult tickets cost $7.50 and children's ticket cost $4.50 how many of each kind of ticket were sold?

544 adult tickets and 106 children's tickets were sold.

Step-by-step explanation:

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

Let y represent the number of children's tickets that were sold.

Adult tickets cost $7.50 and children's ticket cost $4.50. The manager of the movie theater found that Saturday's sales were $3657. It means that

7.5x + 4.5y = 3657- - - - - - - - - - 1

He knew that a total of 650 tickets were sold Saturday. It means that

x + y = 650

Substituting x = 650 - y into equation 1, it becomes

7.5(650 - y) + 4.5y = 3657

4875 - 7.5y + 4.5y = 3657

- 7.5y + 4.5y = 3657 - 4875

3y = 1218

y = 318/3

y = 106

x = 650 - y = 650 - 106

x = 544