There are tickets for 14$, 20$, and 50$. the amount of 14$ tickets is 5 times that of the amount of 50$ tickets. the amount of 14$ tickets is 15 more than the sum of the 20$ and 50$ tickets. all the tickets add up to be 11,700$. find the quantity of each ticket.
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1) Let the number of 50$ tickets be x
==> 14$ tickets = 5x
2) If the number of 20$ tickets = y, then x + y + 15 = 5x
==> y = 4x - 15.
3) Total value of the tickets = 14(5x) + 20(4x - 15) + 50x = 11700$
==> (70x + 80x + 50x - 300)$ = 11700$
==> 200x = 12000
==> x = 60
Hence, there are 60 numbers of 50$ tickets; 300 numbers of 14$ tickets and 225 numbers of 20$ tickets.
==> 14$ tickets = 5x
2) If the number of 20$ tickets = y, then x + y + 15 = 5x
==> y = 4x - 15.
3) Total value of the tickets = 14(5x) + 20(4x - 15) + 50x = 11700$
==> (70x + 80x + 50x - 300)$ = 11700$
==> 200x = 12000
==> x = 60
Hence, there are 60 numbers of 50$ tickets; 300 numbers of 14$ tickets and 225 numbers of 20$ tickets.