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.