A movie theater sells two types of tickets, adult tickets for $12 and child tickets for $8. If the theater sold 30 tickets for a total of $300, how much was spent on Adult Tickets?

The answer is $180.

Explanation:

Since we have two different ticket types, let's say that adult tickets represent x, and children tickets represent y. In this case, the total price would be 12x+8y that is equal to $300. We have total of 30 tickets, too. Well, then x+y should be equal to 30. Our equation system turns out to this:

12x+8y=300

x+y=30

Since we're finding the x, that is the adult tickets, we need to eliminate y by multiplying the second equation by -8. When you do that,

12x+8y=300

-8x-8y=-240

Now, you can add them.

Those y's will cancel out, and we'll be left with,

12x-8x=60

4x=60

x=15

So we found x. Let's think, the adult tickets price was $12 per. We can say that the adult tickets' price will be,

12x

In this case, 12.15 will be our answer.

It's $180.

Let's demonstrate that we found the right answer,

8y=120

y=15 too.

That assures the second equation that is 15+15=30.