SOLUTION: tickets for a certain concert sold for $6, $8 and 12$ each. there were 280 more 6$ tickets sold than 8$ and 12$ tickets together and the total revenue from 840 tickets was $6080.

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Question 1082541: tickets for a certain concert sold for $6, $8 and 12$ each. there were 280 more 6$ tickets sold than 8$ and 12$ tickets together and the total revenue from 840 tickets was $6080. how many tickets were sold?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39616)   (Show Source): You can put this solution on YOUR website!

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
Let  x = # of $8 tickets and y = # of $12 tickets.

Then the number of $6 tickets is (x+y+280).


The "items" equation is

(x + y + 280) + x + y = 840,    (1)


The "value" equation is

6(x+y+280) + 8x + 12y = 6080.   (2)


Simplify

 2x +  2y =  560            (560 = 840-280)
14x + 18y = 4400            (4400 = 6080-6*280)

Or even better

 x +  y = 280
7x + 9y = 2200.

Solve by any method you know (substitution, elimination).


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