Say the amount of money in the original pile was "x". Then the inequality we can set up is x >= 200
80 is in the left pocket
(x - 80)/3 is the amount given away, and x - 80 - (x-80)/3 is the amount in the right pocket.
Total amount of money left over would be 80 + (x - 80 - (x-80)/3) > x - 200
x - (x-80)/3 > x - 200
(80-x)/3 > -200
80 - x > -600
200 =< x < 680
x = [200, 680)
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So the answer is 16sqrt(3) units^2