document.write( "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.
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Algebra.Com's Answer #508619 by KMST(5328) $\"\"$ $\"About$

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$\"x\"$ = number of mangoes each friend should get if divided fairly.
\n" ); document.write( " $\"3x\"$ = number of mangoes stolen.
\n" ); document.write( "Friend number 1, reaches agreed meeting point, takes $\"x\"$ mangoes and runs away.
\n" ); document.write( "There are $\"2x\"$ mangoes left at the meeting point.
\n" ); document.write( "Friend number 2, finds $\"2x\"$ mangoes.
\n" ); document.write( "Not knowing that friend number 1 has already taken $\"1%2F3\"$ of the stolen mangoes,
\n" ); document.write( "friend number 2 tries to figure out how to divide $\"2x\"$ into 3 equal portions.
\n" ); document.write( " $\"2x\"$ cannot be divided evenly, but setting aside $\"1\"$ of the mangoes,
\n" ); document.write( " $\"2x-1\"$ can be evenly divided into 3 equal portions of $\"%282x-1%29%2F3\"$ .
\n" ); document.write( "Friend number 2 decides that the other 2 friends will be satisfied with $\"%282x-1%29%2F3\"$ mangoes,
\n" ); document.write( "takes $\"%282x-1%29%2F3\"$ plus the $\"1\"$ mango set aside,
\n" ); document.write( "and happily leaves with $\"%282x-1%29%2F3%2B1\"$ mangoes.
\n" ); document.write( "Coincidentally, the amount that friend number 2 took is exactly $\"x\"$ .
\n" ); document.write( " $\"highlight%28%282x-1%29%2F3%2B1=x%29\"$ is our equation.
\n" ); document.write( "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.
\n" ); document.write( " $\"%282x-1%29%2F3%2B1=x\"$
\n" ); document.write( "Subtracting $\"1\"$ from both sides of the equal sign, we get
\n" ); document.write( " $\"%282x-1%29%2F3=x-1\"$
\n" ); document.write( "Multiplying times $\"3\"$ both sides of the equal sign, we get
\n" ); document.write( " $\"2x-1=3%28x-1%29\"$
\n" ); document.write( "Applying the distributive property to the $\"3%28x-1%29\"$ we get
\n" ); document.write( " $\"2x-1=3x-3\"$
\n" ); document.write( "Adding $\"3\"$ to both sides of the equal sign, we get
\n" ); document.write( " $\"2x-1%2B3=3x-3%2B3\"$ --> $\"2x%2B2=3x\"$
\n" ); document.write( "Subtracting $\"2x\"$ from both sides of the equal sign, we get
\n" ); document.write( " $\"2x-2x%2B2=3x-2x\"$ --> $\"2=%283-2%29x\"$ --> $\"2=1%2Ax\"$ --> $\"highlight%28x=2%29\"$
\n" ); document.write( "So $\"3x=3%2A2=highlight%286%29\"$ .
\n" ); document.write( "Friend number 1 had taken $\"6\"$ mangoes when he had to run away because the garden's owner was approaching.
\n" ); document.write( "Friend number 1 took $\"6%2F3=2\"$ mangoes, leaving $\"6-2=4\"$ mangoes left for the other two friends.
\n" ); document.write( "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.
\n" ); document.write( "So friend number 2 took $\"2\"$ mangoes (the 1 mango \"fair share\" plus the leftover mango), leaving $\"4-2=2\"$ mangoes behind.
\n" ); document.write( "Friend number 3 took those $\"2\"$ mangoes, assuming that the other two had already taken their share.\r
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