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) About Me  (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" -----> x%2By=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%2B6y=272000






So we have the system of equations:

system%28x%2By=32000%2C14x%2B6y=272000%29



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=32000 Start with the first equation


y=32000-x Subtract x from both sides


y=-x%2B32000 Rearrange the equation


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

Since y=-x%2B32000, we can now replace each y in the second equation with -x%2B32000 to solve for x



14x%2B6highlight%28%28-x%2B32000%29%29=272000 Plug in y=-x%2B32000 into the second equation. In other words, replace each y with -x%2B32000. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



14x%2B%286%29%28-1%29x%2B%286%29%2832000%29=272000 Distribute 6 to -x%2B32000


14x-6x%2B192000=272000 Multiply


8x%2B192000=272000 Combine like terms on the left side


8x=272000-192000Subtract 192000 from both sides


8x=80000 Combine like terms on the right side


x=%2880000%29%2F%288%29 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%2B32000 (remember we previously solved for y in the first equation).



y=-x%2B32000 Start with the equation where y was previously isolated.


y=-%2810000%29%2B32000 Plug in x=10000


y=-10000%2B32000 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.

Answer by Mathtut(3670) About Me  (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
:
highlight%28y=10000%29 number of $14 tickets
:
highlight%28x=32000-10000=22000%29number of $6 tickets