Question 282360
Let x = the number of apples there were originally.


First man eats 1/3 * x, so you are left with 2/3 * x


Second man eats 1/3 * 2/3 * x which equals 2/9 * x.


2/3 * x - 2/9 * x equals 6/9 * x - 2/9 * x equsls 4/9 * x


Third man eats 1/3 * 4/9 * x which equals 4/27 * x.


4/9 * x - 4/27 * x equals 12/9 * x - 4/27 * x equals 8/27 * x


After everybody gets their fill, you are left with 8/27 * x


Since there are 8 apples left, this means that 8/27 * x = 8


Multiply both sides of this equation by 27 to get:


8 * x = 27 * 8


Divide both sides of this equation by 8 to get:


x = 27


The original number of apples is 27.


To prove, substitute 27 for x and go through the original problem again.


There are 27 apples.


First man eats 1/3 * 27 = 9.


27 - 9 = 18


Second man eats 1/3 * 18 = 6.


18 - 6 = 12.


Third man eats 1/3 * 12 = 4.


12 - 4 = 8


There are 8 apples left when the original number is 27.


That's your answer.


I also looked at it again and solved it this way:


x - (1/3)x = (2/3)x = a
a - (1/3)a = (2/3)a = b
b - (1/3)b = (2/3)b = c


I got:


(2/3)x = a
(2/3)a = b
(2/3)b = c


Working back from (2/3)b = c, I then substituted (2/3)a for b and got:


(2/3)*(2/3)*a = c


I then substituted x for a to get:


(2/3)*((2/3)*2/3)*x = c


I simplified this to get:


(8/27)x = c


Since c = 8 which was the number of apples left after everybody had their fill, I got:


(8/27)x = 8


I multiplied both sides of this equation by 27 to get:


8x = 8*27


I divided both sides of this equation by 8 to get:


x = 27.


That's your answer again looking at it a slightly different way.