Question 170428
Let x=# of reserved tickets  and y = # of general admission tickets


Total number of people equation:

"There are 32,000 fans at a football game" -----> {{{x+y=32000}}}




Total Revenue equation:

"The total of ticket sales was #272,000" and "reserved tickets for $14 and how many got general adission for $6.00" translates to {{{14x+6y=272000}}}







So we have the system of equations:


{{{system(x+y=32000,14x+6y=272000)}}}




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=32000}}} Start with the first equation



{{{y=32000-x}}}  Subtract {{{x}}} from both sides



{{{y=-x+32000}}} Rearrange the equation



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


Since {{{y=-x+32000}}}, we can now replace each {{{y}}} in the second equation with {{{-x+32000}}} to solve for {{{x}}}




{{{14x+6highlight((-x+32000))=272000}}} Plug in {{{y=-x+32000}}} into the second equation. In other words, replace each {{{y}}} with {{{-x+32000}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{14x+(6)(-1)x+(6)(32000)=272000}}} Distribute {{{6}}} to {{{-x+32000}}}



{{{14x-6x+192000=272000}}} Multiply



{{{8x+192000=272000}}} Combine like terms on the left side



{{{8x=272000-192000}}}Subtract 192000 from both sides



{{{8x=80000}}} Combine like terms on the right side



{{{x=(80000)/(8)}}} Divide both sides by 8 to isolate x




{{{x=10000}}} Divide






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



So the first part of our answer is: {{{x=10000}}}










Since we know that {{{x=10000}}} we can plug it into the equation {{{y=-x+32000}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-x+32000}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-(10000)+32000}}} Plug in {{{x=10000}}}



{{{y=-10000+32000}}} Multiply



{{{y=22000}}} Combine like terms 




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



So the second part of our answer is: {{{y=22000}}}










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


So our answers are:


{{{x=10000}}} and {{{y=22000}}}



Which means that 10,000 reserved tickets were sold and 22,000 general admission tickets were sold.