SOLUTION: At a college play production, 360 tickets were sold. The ticket prices were $8, $10, and $12 and the total income from ticket sales was 3436. How many tickets of each type were wol

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Question 1115646: At a college play production, 360 tickets were sold. The ticket prices were $8, $10, and $12 and the total income from ticket sales was 3436. How many tickets of each type were wold if the number of $8 tickets sold was twice the number of $12 tickets sold?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x of the $10 tickets
y of the $12 tickets
2y of the $8 tickets

system%282y%2Bx%2By=360%2C8%2A2y%2B10x%2B12y=3436%29

system%28x%2B3y=360%2C10x%2B28y=3436%29

system%28x%2B3y=360%2C5x%2B14y=1718%29

system%285x%2B15y=1800%2C5x%2B14y=1718%29
Subtract corresponding members.

highlight%28y=82%29------------quantity of the $12 tickets
Use this to find x and 2y.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

                It is a typical problem to solve using a single unknown. 


Let x = # of $12 tickets.

Then the number of $8 tickets is 2x, according to the condition.

Then the number of $10 tickets is  (360 - x - 2x) = (360-3x).


Now your "money" equation is


8*(2x) + 10*(360-3x) + 12*x = 3436,   or


16x + 3600 - 30x + 12x = 3436

-2x = 3436 - 3600 = - 164  ====>  x = 82.


Answer.  82 $12 tickets;  2*82 = 164 $8 tickets;  and  (360-3*82) = 114 $10 tickets.


Check.   12*82 + 8*164 + 10*114 = 3436 dollars.    ! Correct !