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Hi,
Let x represent the number of tickets in the beginning
If I am understanding the question properly:
selling 1/2 of your tickets and giving away 1/4 of the rest = 3600 tickets
x/2 + 1/4(x/2) = 3600
(1/2)x + (1/8)x = 3600
(5/8)x = 3600
x = 3600(8/5)
x = 5760, the number of tickets in the beginning