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?

Answer:

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.

The Amount spent on adult tickets in the movie theater from the given parameters is: $180

Let's assume the number of adult tickets sold is A and the number of child tickets sold is C.

We are given that:

- The price of an adult ticket is $12, and as such the revenue from selling adult tickets would be 12A dollars.

- The price of a child ticket is $8, so the revenue from selling child tickets would be 8C dollars.

- The total number of tickets sold is 30, so A + C = 30.

The total revenue from selling all the tickets is $300.

We can create two equations to represent the above information:

Equation 1: 12A + 8C = 300 (total revenue equation)

Equation 2: A + C = 30 (total number of tickets equation)

Now, let's solve this system of equations to find the values of A and C:

First, we can solve Equation 2 for C:

C = 30 - A

Next, substitute this value of C into Equation 1:

12A + 8(30 - A) = 300

Now, simplify and solve for A:

12A + 240 - 8A = 300

4A = 300 - 240

4A = 60

A = 60 / 4

A = 15

So, 15 adult tickets were sold. To find out how much was spent on adult tickets, we multiply the number of adult tickets (15) by the price of an adult ticket ($12):

Amount spent on adult tickets = 15 * $12 = $180.

Therefore, $180 was spent on adult tickets.

Read more about Algebra Word problems at: https://brainly.com/question/21405634

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