April sold 75 tickets to a school play and collected a total of $495. If the adult tickets cost $8 each and child tickets cost $5 each, how many adult tickets and how many child tickets did she sell?

40 adult tickets and 35 child tickets were sold.

Step-by-step explanation:

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

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

April sold 75 tickets to a school play. It means that

x + y = 75

If the adult tickets cost $8 each and child tickets cost $5 each and and a total of $495 was collected from ticket sales, it means that

8x + 5y = 495- - -- - - - - - - - -1

Substituting x = 75 - y into equation 1, it becomes

8(75 - y) + 5y = 495

600 - 8y + 5y = 495

- 8y + 5y = 495 - 600

- 3y = - 105

y = - 105/-3

y = 35

x = 75 - y = 75 - 35

x = 40