Question 237340: Please help me understand how to solve the following problem?
Three tired and hungry people had a big bag of apples. While the other two were asleep, one of the three awoke, ate one-third of the apples, and went back to sleep. Later a second person awoke, ate one-third of the remaining apples and went back to sleep. Finally, the third person awoke and ate one-third of the remaining apples, leaving 8 apples in the bag. How many apples were in the bag originally?
Found 2 solutions by edjones, rapaljer:
Answer by edjones(8007)   (Show Source):
Answer by rapaljer(4671)  (Show Source):
You can put this solution on YOUR website! 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:
Multiply both sides of the equation by the reciprocal of (8/27) which is (27/8), and you have
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
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