Question

Adam, Bryant and Clara shared some pies. Adam ate 2/3 of the number of pies 
  and 2/3 of a pie. Bryant then ate 2/3 of the remaining number of pies and 2/3 of a 
pie. Finally, after Bryant had eaten his pies. Clara ate 2/3 of the remaining 
number of pies and 2/3 of a pie.  There was no pie left.
(a) How many pies were there at first?
(b) How many pies did Bryant eat?

Answer 1

very confusing pie eating event.

Assume all the pies are the same , let x represent the number of pies
Adam ate: (2/3)(x) + (2/3) = (2/3)(x + 1)
Pies left = x - (2/3)(x+1)
= x - 2/3 x - 2/3 = 1/3 x - 2/3 = (x-2)/3

Bryant ate: (2/3)(x-2)/3 + 2/3
= 2/9 x - 4/9 + 2/3
= 2/9 x + 2/9
pies left over after that:
= (1/3 x - 2/3) - (2/9 x + 2/9)
= 1/9 x - 8/9

Clara ate: (2/3)((1/9 x - 8/9) + 2/3
= 2/27 x - 16/27 + 2/3
= 2/27 x + 2/27

pies left over after that
= 1/9 x - 8/9 - 2/27 x - 2/27
= 1/27 x - 26/27
this is supposed to be equal to zero

1/27 x = 26/27
x = 26

so we started with 26 pies, and Bryant ate
2/9 x + 2/9
= (2/9)(26) + 2/9 = 6 pies

Answer 2

Thank u very much

Answer 3

Let number of pies = X
Adam : 2/3X + 2/3
Bryant : 2/5 (X-Adam) + 2/3
= 2/3 (1/3x - 2/3) + 2/3
= 2/9x - 4/9 + 6/9 = 2/9x + 2/9
Clara = 2/3 (X-Adam-Bryant) + 2/3
= 2/3 (1/3x - 2/3 - 2/9x - 2/9) + 2/3 = 2/3 (1/9x - 8/9) + 2/3
= 2/27x + 2/27
A + B + C = 2/27x + 2/27 + 2/9x + 2/9 + 2/3x + 2/3 = x
26/27x + 26/27 = x
1/17x = 26/27
X = 26 (a)

(2/9)(26)+2/9 = 6 (b)