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).