SOLUTION: From a basket of mangoes, the King took 1/6, the Queen took 1/5 of the remainder, the three chief Princes to ¼, 1/3, and ½ of the successive remainders, respectively. The youngest

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: From a basket of mangoes, the King took 1/6, the Queen took 1/5 of the remainder, the three chief Princes to ¼, 1/3, and ½ of the successive remainders, respectively. The youngest       Log On


   

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 ¼, 1/3, and ½ 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) About Me  (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 ¼, 1/3, and ½ 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
5%2F6 * 4%2F5 * 3%2F4 * 2%2F3 * 1%2F2x = 3
120%2F720x = 3
reduce fraction
1%2F6x = 3
multiply both sides by 6
x = 18 mangoes originally

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
%285%2F6%29%2A%284%2F5%29%2A%283%2F4%29%2A%282%2F3%29%2A%281%2F2%29%2Ax=3
%285%2A4%2A3%2A2%2A1%2F%286%2A5%2A4%2A3%2A2%29%29%2Ax=3
There is 5, 4, 3, and 2 in numerator and denominator.
They "cancel out" and you get
%281%2F6%29%2Ax=3 so x=3%2A6 and highlight%28x=18%29 .
The interesting part is that the king took 1%2F6 of 18 mangoes,
which is %281%2F6%29%2A18=3 mangoes,
and each person after the king took 3 mangoes too.
of the 18-3=15 mangoes left, the queen took
%281%2F5%29%2A15=3 mangoes, leaving
15-3=12 .
Then from those 12 the first prince took 1%2F4,
which was %281%2F4%29%2A12=3 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 n family members that had not yet received a portion, and took the 1%2Fn fair share, so they would all end up with the same amount.