SOLUTION: I am coming up with crazy answers to this question. Please help me get the right answer. There are 32,000 fans at a football game. The total of ticket sales was #272,000. How many

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Question 170428: I am coming up with crazy answers to this question. Please help me get the right answer. There are 32,000 fans at a football game. The total of ticket sales was #272,000. How many fans paid for reserved tickets for $14 and how many got general adission for $6.00 a ticket?
Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
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" ----->



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






So we have the system of equations:





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

Start with the first equation


Subtract from both sides


Rearrange the equation


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

Since , we can now replace each in the second equation with to solve for



Plug in into the second equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.



Distribute to


Multiply


Combine like terms on the left side


Subtract 192000 from both sides


Combine like terms on the right side


Divide both sides by 8 to isolate x



Divide





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


So the first part of our answer is:









Since we know that we can plug it into the equation (remember we previously solved for in the first equation).



Start with the equation where was previously isolated.


Plug in


Multiply


Combine like terms



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


So the second part of our answer is:









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

So our answers are:

and


Which means that 10,000 reserved tickets were sold and 22,000 general admission tickets were sold.
Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!
lets call the number of $6 tickets x and the number of $14 tickets y.
:
x+y=32000.....eq 1---->x=32000-y
6x+14y=272000.eq 2
:
take x's value from eq 1 and plug it into eq 2
:
6(32000-y)+14y=272000
:
192000-6y+14y=272000
:
8y=80000
:
number of $14 tickets
:
number of $6 tickets
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