Given: Let x be the whole amount inherited. 1/2 * x - invested with Bernie Madoff 1/3 * x - lost due to identity theft 1/8 * x - lost in casino 40,000 - remainder
x = 960,000 initial inheritance x/2 = 960,000/2 = 480,000 invested with Bernie Madoff x/3 = 960,000/3 = 320,000 lost due to identity theft x/8 = 960,000/8 = 120,000 lost in the casino 40,000 - remaining amount.
Well, you only listed three pieces so far. But I can already see a pattern emerging from those three.
Of course, the next piece might return to 1-1/2 inches. I mean, the pattern can't just keep on going and increasing forever or Cody would eventually wind up with pieces that are a mile long. It must eventually return to 1-1/2 inches and start over from there.
From the first piece to the second one, and from the second one to the third one, the increase is 5/16 inch both times. So if the pattern is more than three pieces long before it starts over from 1-1/2, then the next piece is
