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.
