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

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) (Show Source): You can put this solution on YOUR website!
= number of mangoes each friend should get if divided fairly.
= number of mangoes stolen.
Friend number 1, reaches agreed meeting point, takes mangoes and runs away.
There are mangoes left at the meeting point.
Friend number 2, finds mangoes.
Not knowing that friend number 1 has already taken of the stolen mangoes,
friend number 2 tries to figure out how to divide into 3 equal portions.
cannot be divided evenly, but setting aside of the mangoes,
can be evenly divided into 3 equal portions of .
Friend number 2 decides that the other 2 friends will be satisfied with mangoes,
takes plus the mango set aside,
and happily leaves with mangoes.
Coincidentally, the amount that friend number 2 took is exactly .
is our equation.
By lucky coincidence, friends 1 and 2 took their fair share of mangoes each, and there are mangoes left for friend number 3.

Subtracting from both sides of the equal sign, we get

Multiplying times both sides of the equal sign, we get

Applying the distributive property to the we get

Adding to both sides of the equal sign, we get
-->
Subtracting from both sides of the equal sign, we get
--> --> -->
So .
Friend number 1 had taken mangoes when he had to run away because the garden's owner was approaching.
Friend number 1 took mangoes, leaving mangoes left for the other two friends.
Friend number 2, assuming that those mangoes was all that had been stolen, realized that 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 mango left.
So friend number 2 took mangoes (the 1 mango "fair share" plus the leftover mango), leaving mangoes behind.
Friend number 3 took those mangoes, assuming that the other two had already taken their share.

RELATED QUESTIONS
Theresa has two baskets of mangoes. She has a total of 90 mangoes. The number of mangoes (answered by josmiceli)

PLEASE HELP !How many dozen mangoes are there in 72x2... (answered by fractalier)

Use Matrices to solve this problem. Baskets of fruit are prepared for sale at a... (answered by josgarithmetic)

if three mangoes are taken one after the other from a basket which contains 10 ripe and (answered by Edwin McCravy)

In a basket full of balls, 60% are mangoes and remaining 40% are apple. 25% of apples are (answered by greenestamps,ikleyn)

Mang Ben has 40 seedlings to plant 1/4 of them are mangoes, 3/8 are avocados and the rest (answered by ikleyn)

Mark bought some fruits 1/5 of the fruits are avocados 1/3 are star apples and 2/7 of the (answered by Fombitz)

There are 3 mangoes, 4 Guava & 5 oranges.In how many ways can they be arranged in a... (answered by sudhanshu_kmr)

In a large consignment of mangoes 2% are rotten. What is the probability that a carton... (answered by stanbon)