SOLUTION: Three tired and hungry people had a bag of apples. while the other two were alseep, one of the three awoke, ate one-third of the apples, and went back to sleep. Later a second pers

Algebra ->  Algebra  -> Percentage-and-ratio-word-problems -> SOLUTION: Three tired and hungry people had a bag of apples. while the other two were alseep, one of the three awoke, ate one-third of the apples, and went back to sleep. Later a second pers      Log On

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Question 239518: Three tired and hungry people had a bag of apples. while the other two were alseep, 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, a 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?
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If person 3 had 8 apples left after eating one-third of what remained, then 8 must be two-thirds of what remained. Let be the number of apples in the bag before ThirdPerson started to eat. Then:



Once you solve for , you can apply the same logic to figure out what was in the bag before SecondPerson started eating, and then repeat the process one more time to figure out what was in the bag before FirstPerson started to eat, which is the original number of apples in the bag.


John