Sophia.13
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
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Dido525
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Do you realize you have to make a system of equations?
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@Sophia.13
Dido525
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You there? :P .
Sophia.13
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Sorry, yeah I'm here and no.. i dont know what to do at all. /:
Dido525
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Okay you have two situations, whenever you have 2 situations you usually have to make a system of equations.
Dido525
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First of all do you KNOW what a system of equations is?
Sophia.13
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Okay, and no..
Dido525
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It's where you work with two equations and different variables.
Dido525
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For example like:
|dw:1356304863230:dw|
Sophia.13
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ohh ok
Dido525
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Do you understand?
Sophia.13
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kinda
Dido525
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The idea for a system of equations is to solve for both of the variables.
Sophia.13
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ohh okkay i get it
Dido525
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So I said:
|dw:1356304949957:dw|
Dido525
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Since you are just learning this we will use substitution.
Sophia.13
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ok
Dido525
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BTW this is NOT the question. It's just an example.
Dido525
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By substitution I mean that you make one variable in terms of another variable.
Dido525
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Does that make sense?
Sophia.13
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Yeah
Dido525
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|dw:1356305047829:dw|
Dido525
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Does that make sense?
Sophia.13
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kiinda
Dido525
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Okay, what is it you don't get? :)
Sophia.13
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Its just a little confusing hah, but i think i it now.
Dido525
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Are you sure? :) . I got time. I can explain if you really need to :) .
Dido525
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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.
Dido525
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Does that make sense?
Sophia.13
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Why dont u just use x instead of substituting it with y?
Dido525
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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.
Dido525
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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.
Dido525
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Does that make sense? :) .
Sophia.13
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yeah, but i just dont understand why you need to substitute x with y instead of just keeping x, x?
Dido525
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Okay, think of it this way. Do you know what x is equal to?
Sophia.13
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no
Dido525
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We aren't given any values for x at all.
Sophia.13
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oh
Dido525
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So how would you solve for x unless you get rid of it somehow? :) .
Dido525
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Does that make sense?
Sophia.13
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Oh i get it nowww
Dido525
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Good! :D .
Dido525
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Okay then. So we have:
|dw:1356305797768:dw|
|dw:1356305817320:dw|
Dido525
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Wait wait!!! That's not the question!!! :P . I just provided an example.
Dido525
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|dw:1356305892765:dw|
Dido525
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@Sophia.13 : Now shall we work on your question together? :) .
Sophia.13
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Okay.(:
Dido525
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Let the children's ticket's price be x
Let the adult's ticket's price be y.
Dido525
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Do you get that?
Sophia.13
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Yeah
Dido525
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One second. Can you hold on? I need to actually do this out myself ^_^ .
Dido525
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Ohh sorry let's switch that.
Let the adult's ticket's price be x
Let the children's ticket's price be y.
Dido525
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Do you get that?
Dido525
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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.
Dido525
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Does that make sense?
Sophia.13
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yeah that makes sense
Dido525
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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.
Dido525
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So can you see a way to make an equation from that?
Dido525
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Let the adult's ticket's price be x
Let the children's ticket's price be y.
Sophia.13
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56x + 112y = 896 ?
Dido525
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Excellent job!
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Now in the second opening week, there were 23 adults and 92 kids and there tickets equaled a total of $552.
Dido525
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Can you make an equation from that?
Sophia.13
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23x + 92y = 552 ? c:
Dido525
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Very good! :) .
Dido525
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So we have:
|dw:1356306963125:dw|
Dido525
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Now, we don't what any of the prices are so we have to get rid of one of the variables.
Dido525
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Do you understand? :) .
Dido525
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Now, we don't know*
Sophia.13
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Yeah i understand.
Dido525
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Now let's pick the first equation. Can you solve for x? :) .
Dido525
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Aww shucks. :P . Thanks for the fanning.
Sophia.13
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No problem C:
Dido525
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yes, there is going to be a bunch of ugly fractions involved.
Sophia.13
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I dont exactly remember how to solve for x.. i swear my brain just went through a time warp and lost my mathematical memory -___-
Dido525
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It's okay... :) .
|dw:1356307195870:dw|
Dido525
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Now what would you do? :) .
Sophia.13
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Um..for 56x = 896-112y dive both sides of the equation by 56?
Dido525
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yep :) .
Dido525
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See? You remember just fine :) .
Dido525
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So x equals...? :)
Sophia.13
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Hah so x = 16 - 112y? i dont think thats right is it?
Dido525
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No :3 .
|dw:1356307670894:dw|
Dido525
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I tend to avoid simplyfing. Don't ask why.
Sophia.13
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Ohhhhh that makes sense. :P
Dido525
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Now we know what x equals in terms of y.
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We have:
|dw:1356307766229:dw|
Dido525
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We know what x equals. Can you substitute for x? :) .
Dido525
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Yes, there is an ugly fraction involved.
Sophia.13
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I dont know what to do .-.
Dido525
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Okay so we have:|dw:1356308102259:dw|
Dido525
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We know x equals
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|dw:1356308121223:dw|
Sophia.13
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hold on a sec please. I'll brb(:
Dido525
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Substitute for x.
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Okay :) .
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|dw:1356308143795:dw|