Tickets to a 3D movie cost $12.50 for adults and $8.50 for children. The theater can seat up to 180 people. A total of $1826 was collected in ticket sales for the sold out 7:15 PM show. Determine the number of adult tickets and the number of children's tickets that were sold.

Let, number of children are x and number of adult are y.

Total number of seats, T = 180.

x + y = 180     1)

Tickets to a 3D movie cost $12.50 for adults and $8.50 for children.

So, total amount :

8.5x + 12.5y = A

8.5x + 12.5y = 1826    2)

Solving equation 1) and 2) , we get :

8.5x + 12.5( 180 - x ) = 1826

8.5x - 12.5x + 2250 = 1826

-4x = -424

x = 106

y = 180 - 106 = 74

Therefore, the number of adult tickets and the number of children's tickets that were sold are 74 and 106.

Hence, this is the required solution.

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1: -2 3/4, -2 1/2, -14, 0, 3, 8 1/3

2: -4, -3, -2 1/2, -2 1/4, 3 1/4,

step-by-step explanation: