PLEASE DON'T SKIP MY QUESTION SUPER IMPORTANT I AM SO LOST AND CONFUSED At a movie theater, the price of 2 adult tickets and 4 child tickets is $48. The price of 5 adult tickets and 2 child tickets is $64. Let x be the cost of an adult ticket and let y be the cost of a child ticket. Write and solve a system of equations to find the ticket price for one adult and for one child.

The answer is $10 per adult ticket, and $7 per child ticket. Now lets figure out how to get to that answer. Let's create a chart to help visualize this.

- - - - -A- - - - - C- - - - -T- - - - -

    :     2    :      4     :   $48    :    

    :     5    :        2   :   $64    :                Key:

    :           :             :               :                      A = Adult ( The Y)

    :           :             :               :                      C = Child ( The X)

    :           :             :               :                       T= Total

When we look at it, the total cost is less then what the adult would be when multiplied by 10, and you WOULD have to add the children cost to the adult cost, so lets try it.

Lets do the 2 adult tickets first, 2 x 10 is 20. Now we do 48 - 20 to get how much the cost of the children's 4 needs to equal. We get 28 as the answer. Now we have to do 28 divided by 4, we get 7 as that answer.

Now lets plug that in to the $64 problem and see if that gets us the correct answer.

So the amount of adult tickets for this problem is 5, so we do 5 x 1 which is 50.

Now the amount of children tickets is 2, so lets do 2 x 7, which equals 14.

Now to test if it gets us the correct answer, to do that we do 50 + 14, that equals what we want it to, 64.

Therefor, the correct answer is $10 per adult ticket, and $7 per child ticket.

Hope this helps!

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

ok

step-by-step explanation: