SOLUTION: Hi, I have the answers to the problems but I don't know the steps to get the answer here are a few of my word problems and answers. If someone could help me out with the formula t

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Question 143643: Hi, I have the answers to the problems but I don't know the steps to get the answer here are a few of my word problems and answers. If someone could help me out with the formula to answer the problem it would be greatly appreciated.
Six hundred people attened the premiere of a motion picture. Adult tickets cost $9, and chilren were admitted for $6. If box office reciepts totaled $4800, how many chilren attended the premiere?

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=# of children, y=# of adults

Since "Six hundred people attened the premiere", this means that the total of children and adults is 600. So the first equation is: x%2By=600


Also, since "Adult tickets cost $9, and chilren were admitted for $6" and the theater pulled in $4,800, this tells us that the second equation is: 6x%2B9y=4800






So this gives us this system of equations:

system%28x%2By=600%2C6x%2B9y=4800%29



Let's use substitution to solve this system


Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.




So let's isolate y in the first equation

x%2By=600 Start with the first equation


y=600-x Subtract x from both sides


y=-x%2B600 Rearrange the equation


y=%28-x%2B600%29%2F%281%29 Divide both sides by 1


y=%28%28-1%29%2F%281%29%29x%2B%28600%29%2F%281%29 Break up the fraction


y=-x%2B600 Reduce



---------------------

Since y=-x%2B600, we can now replace each y in the second equation with -x%2B600 to solve for x



6x%2B9highlight%28%28-x%2B600%29%29=4800 Plug in y=-x%2B600 into the first equation. In other words, replace each y with -x%2B600. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



6x%2B%289%29%28-1%29x%2B%289%29%28600%29=4800 Distribute 9 to -x%2B600


6x-9x%2B5400=4800 Multiply


-3x%2B5400=4800 Combine like terms on the left side


-3x=4800-5400Subtract 5400 from both sides


-3x=-600 Combine like terms on the right side


x=%28-600%29%2F%28-3%29 Divide both sides by -3 to isolate x



x=200 Divide





-----------------First Answer------------------------------


So the first part of our answer is: x=200









Since we know that x=200 we can plug it into the equation y=-x%2B600 (remember we previously solved for y in the first equation).



y=-x%2B600 Start with the equation where y was previously isolated.


y=-%28200%29%2B600 Plug in x=200


y=-200%2B600 Multiply


y=400 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: y=400









-----------------Summary------------------------------

So our answers are:

x=200 and y=400


So 200 children and 400 adults attended