A children's movie is playing at the local theater.
The first showing earned $896 in ticket sales, and there were 56 adults and 112 children in attendance. The second showing earned $552 in ticket sales, and there were 23 adults and 92 children in attendance.
find the price of an adult's ticket and the price of a child's ticket.
A. Adult: $8.50; Child: $6.25
B. Adult: $8.00; Child: $4.00
C. Adult: $7.00; Child: $6.00
D. Adult: $7.50; Child: $5.75

- anonymous

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- anonymous

Do you realize you have to make a system of equations?

- anonymous

@Sophia.13

- anonymous

You there? :P .

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## More answers

- anonymous

Sorry, yeah I'm here and no.. i dont know what to do at all. /:

- anonymous

Okay you have two situations, whenever you have 2 situations you usually have to make a system of equations.

- anonymous

First of all do you KNOW what a system of equations is?

- anonymous

Okay, and no..

- anonymous

It's where you work with two equations and different variables.

- anonymous

For example like:
|dw:1356304863230:dw|

- anonymous

ohh ok

- anonymous

Do you understand?

- anonymous

kinda

- anonymous

The idea for a system of equations is to solve for both of the variables.

- anonymous

ohh okkay i get it

- anonymous

So I said:
|dw:1356304949957:dw|

- anonymous

Since you are just learning this we will use substitution.

- anonymous

ok

- anonymous

BTW this is NOT the question. It's just an example.

- anonymous

By substitution I mean that you make one variable in terms of another variable.

- anonymous

Does that make sense?

- anonymous

Yeah

- anonymous

|dw:1356305047829:dw|

- anonymous

Does that make sense?

- anonymous

kiinda

- anonymous

Okay, what is it you don't get? :)

- anonymous

Its just a little confusing hah, but i think i it now.

- anonymous

Are you sure? :) . I got time. I can explain if you really need to :) .

- anonymous

Basically, I said that x=5-y from the first equation.
Since I know x=5-y I substituted the x in the second equation with 5-y instead of an x.

- anonymous

Does that make sense?

- anonymous

Why dont u just use x instead of substituting it with y?

- anonymous

The problem with that is that we don't know what x is equal to. So we have to get rid of that x somehow.

- anonymous

From the first equation we are given x+y=5 . So x=5-y
Since we know x=5-y we can substitute that for x in the second equation and solve for y. After solving for y we can solve for x easily afterwards.

- anonymous

Does that make sense? :) .

- anonymous

yeah, but i just dont understand why you need to substitute x with y instead of just keeping x, x?

- anonymous

Okay, think of it this way. Do you know what x is equal to?

- anonymous

no

- anonymous

We aren't given any values for x at all.

- anonymous

oh

- anonymous

So how would you solve for x unless you get rid of it somehow? :) .

- anonymous

Does that make sense?

- anonymous

Oh i get it nowww

- anonymous

Good! :D .

- anonymous

Okay then. So we have:
|dw:1356305797768:dw|
|dw:1356305817320:dw|

- anonymous

Wait wait!!! That's not the question!!! :P . I just provided an example.

- anonymous

|dw:1356305892765:dw|

- anonymous

@Sophia.13 : Now shall we work on your question together? :) .

- anonymous

Okay.(:

- anonymous

Let the children's ticket's price be x
Let the adult's ticket's price be y.

- anonymous

Do you get that?

- anonymous

Yeah

- anonymous

One second. Can you hold on? I need to actually do this out myself ^_^ .

- anonymous

Ohh sorry let's switch that.
Let the adult's ticket's price be x
Let the children's ticket's price be y.

- anonymous

Do you get that?

- anonymous

We know that in the first opening the total earnings for the adults and children combined equaled $896
We also know that in the second opening the total earnings for the adults and children equaled $552.

- anonymous

Does that make sense?

- anonymous

yeah that makes sense

- anonymous

In the first opening there were 56 adults and 112 children and the sum of both of those equaled 896 after they bought there tickets.

- anonymous

So can you see a way to make an equation from that?

- anonymous

Let the adult's ticket's price be x
Let the children's ticket's price be y.

- anonymous

56x + 112y = 896 ?

- anonymous

Excellent job!

- anonymous

Now in the second opening week, there were 23 adults and 92 kids and there tickets equaled a total of $552.

- anonymous

Can you make an equation from that?

- anonymous

23x + 92y = 552 ? c:

- anonymous

Very good! :) .

- anonymous

So we have:
|dw:1356306963125:dw|

- anonymous

Now, we don't what any of the prices are so we have to get rid of one of the variables.

- anonymous

Do you understand? :) .

- anonymous

Now, we don't know*

- anonymous

Yeah i understand.

- anonymous

Now let's pick the first equation. Can you solve for x? :) .

- anonymous

Aww shucks. :P . Thanks for the fanning.

- anonymous

No problem C:

- anonymous

yes, there is going to be a bunch of ugly fractions involved.

- anonymous

I dont exactly remember how to solve for x.. i swear my brain just went through a time warp and lost my mathematical memory -___-

- anonymous

It's okay... :) .
|dw:1356307195870:dw|

- anonymous

Now what would you do? :) .

- anonymous

Um..for 56x = 896-112y dive both sides of the equation by 56?

- anonymous

yep :) .

- anonymous

See? You remember just fine :) .

- anonymous

So x equals...? :)

- anonymous

Hah so x = 16 - 112y? i dont think thats right is it?

- anonymous

No :3 .
|dw:1356307670894:dw|

- anonymous

I tend to avoid simplyfing. Don't ask why.

- anonymous

Ohhhhh that makes sense. :P

- anonymous

Now we know what x equals in terms of y.

- anonymous

We have:
|dw:1356307766229:dw|

- anonymous

We know what x equals. Can you substitute for x? :) .

- anonymous

Yes, there is an ugly fraction involved.

- anonymous

I dont know what to do .-.

- anonymous

Okay so we have:|dw:1356308102259:dw|

- anonymous

We know x equals

- anonymous

|dw:1356308121223:dw|

- anonymous

hold on a sec please. I'll brb(:

- anonymous

Substitute for x.

- anonymous

Okay :) .

- anonymous

|dw:1356308143795:dw|

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