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One night the King couldn't sleep, so he went down into the Royal kitchen, where he found a bowl full of
mangoes. Being hungry, he took 1/6 of the mangoes.
Later that same night, the Queen was hungry and couldn't sleep. She, too, found the mangoes and took 1/5
of what the King had left.
Still later, the first Prince awoke, went to the kitchen, and ate 1/4 of the remaining mangoes.
Even later, his brother, the second Prince, ate 1/3 of what was then left.
Finally, the third Prince ate 1/2 of what was left, leaving only three mangoes for the servants.

How many mangoes were originally in the bowl?

original number of mangoes = x
after king: amount left = 5x/6
after queen amount left : (4/5)(5x/6) = (2/3)x
after prince, amount left = (3/4)((2/3)x = (1/2)x
after 2nd prince, amount left = (2/3(1/2)x = (1/3)x
after 3rd prince, amount left = (1/2)(1/3)x = (1/6)x

(1/6)x = 3
x = 18

check:
king ate 1/6 or 3 leaving 15
queen ate 1/5 or 3 leaving 12
1st prince ate 1/4 or 3 leaving 9
2nd prince ate 1/3 or 3 leaving 6
3rd prince ate 1/2 or 3 leaving 3 for servants.
All is good!

bob

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