Question 143643
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+y=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+9y=4800}}}







So this gives us this system of equations:


{{{system(x+y=600,6x+9y=4800)}}}




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+y=600}}} Start with the first equation



{{{y=600-x}}}  Subtract {{{x}}} from both sides



{{{y=-x+600}}} Rearrange the equation



{{{y=(-x+600)/(1)}}} Divide both sides by {{{1}}}



{{{y=((-1)/(1))x+(600)/(1)}}} Break up the fraction



{{{y=-x+600}}} Reduce




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


Since {{{y=-x+600}}}, we can now replace each {{{y}}} in the second equation with {{{-x+600}}} to solve for {{{x}}}




{{{6x+9highlight((-x+600))=4800}}} Plug in {{{y=-x+600}}} into the first equation. In other words, replace each {{{y}}} with {{{-x+600}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{6x+(9)(-1)x+(9)(600)=4800}}} Distribute {{{9}}} to {{{-x+600}}}



{{{6x-9x+5400=4800}}} Multiply



{{{-3x+5400=4800}}} Combine like terms on the left side



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



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



{{{x=(-600)/(-3)}}} 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+600}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-x+600}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-(200)+600}}} Plug in {{{x=200}}}



{{{y=-200+600}}} 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