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!
it is 18
Thanks...
Well, it seems like those mangoes had quite the royal adventure! Let's do some math and find out how many mangoes were originally in the bowl.
We know that the King took 1/6 of the mangoes, leaving 5/6 of the original amount.
The Queen then took 1/5 of what the King had left, which means she took 1/5 * 5/6 = 1/6 of the original amount.
After the Queen's sneaky snack, there were 4/6 of the original mangoes left.
Next up, the first Prince devoured 1/4 of what was then left, leaving 3/4 * 4/6 = 3/8 of the original amount.
Moving on to the second Prince, he ate 1/3 of what was left, leaving 2/3 * 3/8 = 1/4 of the original amount.
Finally, the third Prince finished off 1/2 of what was left, leaving only 1/2 * 1/4 = 1/8 of the original amount.
And we know that there were three mangoes left for the servants, which is equal to 1/8 of the original amount.
So if we set up the equation, 1/8 of x = 3 (where x is the original amount of mangoes), we can solve for x.
By multiplying both sides by 8/1, we get x = 3 * 8 = 24.
Therefore, there were originally 24 mangoes in the bowl. Let's hope the royals learned to share their snacks more evenly next time!
To find out how many mangoes were originally in the bowl, we need to work backwards from the information given.
Let's start with what happened last. We know that after the third Prince ate 1/2 of what was left, there were only three mangoes remaining. So, if three mangoes are 1/2 of what was left, we can conclude that before the third Prince ate, there were six mangoes.
Now, let's go back to the second Prince. We know that he ate 1/3 of what was left. Since there were six mangoes before the third Prince ate, the second Prince ate 1/3 * 6 = 2 mangoes. So, after the second Prince ate, there were 6 - 2 = 4 mangoes.
Next, we move to the first Prince. We know that he ate 1/4 of what was left. So, before the second Prince ate, there were 4 * 4 = 16 mangoes.
Now it's the Queen's turn. We know that she ate 1/5 of what the King had left. So, before the first Prince ate, there were 16 * 5 = 80 mangoes.
Finally, we have the King. We know that he took 1/6 of the mangoes. So, originally, there were 80 * 6 = 480 mangoes in the bowl.
Therefore, there were originally 480 mangoes in the bowl.