One night, the movie theater sold 715 movie tickets. the ticket prices are shown in the table below. in all, $3,786.50 was taken in. how many of each kind of ticket were sold at the movies? show your work.

movie ticket prices:

adult: $6.50
child: $3.50

a. list the two equations
b. give each type of ticket

Start by writing two equations. For this example let x equal the number of adult tickets and y equal the number of child tickets:
x + y = 715
6.5x + 3.5y = 3,786.5

Inorder to solve for one variable, you need to eliminate the other.
Using the equality property, multiply the first equation by negative 3.5 and add the two equations together:
-3.5x - 3.5y = -2502.5
6.5x + 3.5y= 3,786.5 
The "y" value cancels out and you are left with:
3x = 1284
Use the equality property to divide both sides of the equation by 3 and you are left with: x=428

With this newfound information, plug the x value into the original equation:
6.5(428) + 3.5y = 3,786.5
And solve:
2,782 + 3.5y = 3,786.5
-2,782              -2,782

3.5y = 1004.5
y=287

In short, the theater sold 428 adult tickets and 287 child tickets.