SOLUTION: there are 3 friends going to steal mangoes in garden. 1 go to pick up mangoes. 2nd ,3rd are watching for owner. then owner comes and they ran in different ways. 1 reached at decide

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Question 844222: there are 3 friends going to steal mangoes in garden. 1 go to pick up mangoes. 2nd ,3rd are watching for owner. then owner comes and they ran in different ways. 1 reached at decided point make 3 portions take one and go away. 2nd boy come he make 3 portions of those remaining 2 and take 1part and 1 mango which was not divided on 3 also take with him. 3rd took all of remaining mangoes. next day they found that all of them have same number of mangoes.
---how?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
x= number of mangoes each friend should get if divided fairly.
3x= number of mangoes stolen.
Friend number 1, reaches agreed meeting point, takes x mangoes and runs away.
There are 2x mangoes left at the meeting point.
Friend number 2, finds 2x mangoes.
Not knowing that friend number 1 has already taken 1%2F3 of the stolen mangoes,
friend number 2 tries to figure out how to divide 2x into 3 equal portions.
2x cannot be divided evenly, but setting aside 1 of the mangoes,
2x-1 can be evenly divided into 3 equal portions of %282x-1%29%2F3 .
Friend number 2 decides that the other 2 friends will be satisfied with %282x-1%29%2F3 mangoes,
takes %282x-1%29%2F3 plus the 1 mango set aside,
and happily leaves with %282x-1%29%2F3%2B1 mangoes.
Coincidentally, the amount that friend number 2 took is exactly x .
highlight%28%282x-1%29%2F3%2B1=x%29 is our equation.
By lucky coincidence, friends 1 and 2 took their fair share of x mangoes each, and there are x mangoes left for friend number 3.
%282x-1%29%2F3%2B1=x
Subtracting 1 from both sides of the equal sign, we get
%282x-1%29%2F3=x-1
Multiplying times 3 both sides of the equal sign, we get
2x-1=3%28x-1%29
Applying the distributive property to the 3%28x-1%29 we get
2x-1=3x-3
Adding 3 to both sides of the equal sign, we get
2x-1%2B3=3x-3%2B3 --> 2x%2B2=3x
Subtracting 2x from both sides of the equal sign, we get
2x-2x%2B2=3x-2x --> 2=%283-2%29x --> 2=1%2Ax --> highlight%28x=2%29
So 3x=3%2A2=highlight%286%29.
Friend number 1 had taken 6 mangoes when he had to run away because the garden's owner was approaching.
Friend number 1 took 6%2F3=2 mangoes, leaving 6-2=4 mangoes left for the other two friends.
Friend number 2, assuming that those 4 mangoes was all that had been stolen, realized that 4 could not be divided evenly among the 3 of them. Friend number 2, figured that it would be fair for each friend to get 1 mango, and there would be another 1 mango left.
So friend number 2 took 2 mangoes (the 1 mango "fair share" plus the leftover mango), leaving 4-2=2 mangoes behind.
Friend number 3 took those 2 mangoes, assuming that the other two had already taken their share.