Three adult and three Child movie tickets were purchase for $75 that cost me child tickets $3 less than the cost of an adult ticket
Let the cost of an adult movie ticket be x.
Then the cost of a child movie ticket would be x - $3.
Three adult tickets would cost 3x and three child tickets would cost 3(x - $3).
The total cost is $75, so:
3x + 3(x - $3) = $75
3x + 3x - $9 = $75
6x - $9 = $75
6x = $75 + $9
6x = $84
x = $84 / 6
x = $14
Thus, the cost of an adult movie ticket is $14.
And the cost of a child movie ticket is $14 - $3 = $11. Answer: \boxed{11}.