OK.....here's what I get.......
Let x be the additional amount over the original $200
The greater side of the inequality is
Original pile = (200 + x)
After she gives away $50 she has (150 + x)
And she gives (2/3) of this away = (2/3) (150 + x)
So....she must have (1/3) of this left = (1/3)(150 + x) = amt in her right pocket
The lesser side of the inequality is
(x + 200) - 200 = x
So we have that
[150 + x ] / 3 > x
150 + x > 3x
150 > 2x
75 > x
x < 75
So...I get that the original amount could be on this interval (200 , 275)
