SOLUTION: From a basket of mangoes, the King took 1/6, the Queen took 1/5 of the remainder, the three chief Princes to �, 1/3, and � of the successive remainders, respectively. The youngest

Question 845606: From a basket of mangoes, the King took 1/6, the Queen took 1/5 of the remainder, the three chief Princes to �, 1/3, and � of the successive remainders, respectively. The youngest child took the remaining 3 mangoes. How many mangoes were in the basket originally?
Found 2 solutions by ankor@dixie-net.com, KMST:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
From a basket of mangoes, the King took 1/6, the Queen took 1/5 of the remainder, the three chief Princes to �, 1/3, and � of the successive remainders, respectively.
The youngest child took the remaining 3 mangoes.
How many mangoes were in the basket originally?
:
let x = original number of mangoes
Write an equation using the fractions representing the remaining amts after each operation
* * * * x = 3
x = 3
reduce fraction
x = 3
multiply both sides by 6
x = 18 mangoes originally
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!

There is 5, 4, 3, and 2 in numerator and denominator.
They "cancel out" and you get
so and .
The interesting part is that the king took of mangoes,
which is mangoes,
and each person after the king took mangoes too.
of the mangoes left, the queen took
mangoes, leaving
.
Then from those the first prince took ,
which was mangoes, and so on.
Each member of the family calculated his or her share very fairly.
Each one figured that the remaining mangoes were to be divided among the family members that had not yet received a portion, and took the fair share, so they would all end up with the same amount.
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