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? is there more than one solution?

Question

02-01-2018
Mathematics

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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? is there more than one solution?

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anchitthawi anchitthawi · Answer 1 · 2018-01-02T12:22:01+01:00

if you think in picture, it will be easier
1. king --1/6 of all
2. queen -- 1/5 of what king had left (remaining)
3. 1st prince -- 1/4 of remaining
4. 2nd prince -- 1/3 of remaining
5. 3 rd prince -- 1/2 of remaining
6. there are 3 mangoes left

so if we think that there are 6 parts of all
1. king took 1st part (5 parts left)
2. queen took 1 of what king had left which he left 5 parts (4 parts left)
3. 1st prince took 1 of 4 (3 parts left)
4. 2nd prince took 1 of 3 (2 parts left)
5. 3rd prince took 1 of 2 (1 part left)
that means 1 part equals 3 mangoes
so we have 6 parts at first then there were 18 mangoes originally in the bowl.

i think there is only 1 answer.

KarpaT KarpaT · Answer 2 · 2022-05-31T15:13:29+02:00

There were initially 18 mangoes in the bowl and it is the only solution.

What is a word problem?

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

The bowl is full of mangoes.

Initially consider there are 6 parts of mangoes.

The king took 1/6 of the mangoes, so 5 parts are left.

Then, the queen took 1/5 of what the king had left. So remaining is 4 parts.

Then the first prince took 1/4 of the remaining mangoes. So remaining is 3 parts.

Then the second prince took 1/3 of what was then left. So remaining is 2 parts.

Then the third prince took 1/2 of what was left. So remaining is 1 part.

The remaining left part is only three mangoes for the servants.

⇒ [tex]1 part = 3 mangoes[/tex]

Initially we considered there were 6 parts of mangoes.

Thus, [tex]6 parts = 3(6)[/tex]

⇒ [tex]18 mangoes[/tex]

Hence we can conclude that there were initially 18 mangoes in the bowl and it is the only solution.

Learn more about word problems here

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