Question

7. One night the King could not sleep. He went to the royal kitchen, where he found a bowl full of mangoes. Being hungry, he took 1/6 of the mangoes in the bowl. Later that same night, the Queen could not sleep, and she was hungry. She found the mangoes and took 1/5 of what the King had left in the bowl. Still later, the youngest Prince awoke, went to the kitchen, and ate ¼ of the remaining mangoes. Even later, the second Prince ate 1/3 of what his younger brother had left. Finally, the third Prince, the heir to the throne, ate ½ of what his younger brothers had left, and then there were only three mangoes left in the bowl. How many mangoes were in the bowl when the King found them?

Answer 1

each person took 1/6, so 3 is 16 as well.
There were 18 mangoes to begin

Answer 2

Original number of mangoes = x

after king, amount left:

x - 1 / 6 x = 6 / 6 x - 1 / 6 x = 5 / 6 x

after queen, amount left :

4 / 5 ∙ 5 / 6 x = 4 / 6 x = 2 / 3 x

after youngest prince, amount left:

3 / 4 ∙ 2 / 3 x = 2 / 4 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

Multiply both sides by 6

x = 18

Check Result:

King ate 1 / 6 of 18 = 3

leaving 18 - 3 = 15

Queen ate 1 / 5 of 15 = 3

leaving 15 - 3 = 12

1st prince ate 1 / 4 of 12 = 3

leaving 12 - 3 = 9

2nd prince ate 1 / 3 of 9 = 3

leaving 9 - 3 = 6

3rd prince ate 1 / 2 of 6 = 3

leaving 6 - 3 = 3