how many bananas?

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matherapist

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how many bananas?

Please solve the following problem in an analytic manner. I can solve it by trial and error.

Three men and a monkey live in a treehouse on an island. The men find a nice ripe bunch of bananas but it takes them all day to get up the tree and bring them down. So they decide to go to sleep and divide up the bananas in the morning.

During the night the first man wakes up while the others sleep, looks at the bananas, and decides to take his 1/3 of the bunch. Since the bunch didn\'t divide evenly he gave the extra banana to the monkey. After he fell asleep the second man woke up in the same way and took his third, giving the extra banana to the monkey. Finally the third man woke up and did the same, taking a third of the bananas in the bunch and since it didn\'t divide evenly into three\'s he gave the extra banana to the monkey.

The next morning the men woke up and divided up what was left into three piles, giving the extra banana to the monkey.

What is the least number of bananas that could be in

Posted 230 day ago

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Answers (4)

matherapist

Raj- How do you select the value 21?

Posted 228 day ago

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I will solve this problem analiticaly:
Let x = # of original bananas.
The 1st man gives 1 to the monkey, keeps 1/3 of remaining bananas, and leave 2/3 for others. So:
1st man left (2/3)(x-1), similarly the 2nd man left
(2/3) of [(2/3)(x-1)-1]= (4/9)(x-1)-(2/3) and the 3rd man left (2/3) of [(4/9)(x-1)-(2/3)-1]=
[(8/27)(x-1)-(4/9)-(2/3)]
Then in the morning, the remainder less than 1 was divisible by 3. i.e: it was an integer.
i.e. [(8/27)(x-1)-(4/9)-(2/3)-1] was an integer.
simplifying we get (8x-65)/27 must be an integer.
Or 8x-65 = 27t. for t=21, we get :
8x-65 = 21*27 = 567, or 8x = 632 or x=79<===
Matherapist has shown that 79 is the correct answer.
Solved by rajbaba78.

2nd ma

Posted 229 day ago

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matherapist

math fanatic, The interpretation is your latter one, each man takes 1/3 of the remaining bunch.
79 works
1st guy takes 26 plus 1 leaving 52
2nd takes 17 +1 leaving 34
3rd takes 11 plus 1 leaving 22
next morning each take 7 plus one for the monkey

I'd just like to see an analytic answer

Posted 229 day ago

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math_fanatic

Before I can answer this, I need something clarified. The first man takes a third of the bananas + an extra banana to the monkey. That makes sense.

My question is, does the second (and eventually third) man take a third of the total number of bananas that were in the bunch originally OR does he take a third of the bananas that are left after the first man takes his third?

Posted 229 day ago

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