Question 237340
Let x = original number of apples in the bag 



x-1/3x= 2/3x = number of apples left after the first person 


The second person ate 1/3 of those that were left, so 
1/3*2/3x= 2/9x apples = number of apples eaten by the second person.


This leaves (2/3)x-(2/9)x which is (6/9)x - (2/9)x or 4/9x apples left after the second person.


The third person ate 1/3 of the 4/9x apples, which is 4/27x apples.


This leaves (4/9)x-(4/27)x apples after the third person, which is 
(12/27)x-(4/27)x or (8/27)x.


So the equation is, based upon the number of apples left being equal to 8: 


{{{(8/27)x=8}}}


Multiply both sides of the equation by the reciprocal of (8/27) which is (27/8), and you have


{{{(27/8)*(8/27)x= (27/8)*8}}}
x= 27 apples.


Check:


The first person eats 1/3 of 27 which is 9 apples, leaving 18 apples.

The second person eats 1/3 of 18 which is 6 apples, leaving 12.

The third person eats 1/3 of 12 which is 4 apples, leaving 8 apples.


VERY NICE PROBLEM!!!


Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Altamonte Springs Campus