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.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.