Need help problem solving (math)?

Question

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 left.

Finally, the third prince ate 1/2 of what was left, leaving only three mangoes for the servants.

How many mangoes were orginally in the bowl?

I've worked through this problem a few times and I'm not sure I have the right answer, I just want to compare mine with yours--please tell me how you came up with your answer. Thanks in advance :)

Answer 1

I don't know, but I came up with 1080?? What did you get?

Well this is how I got it. I multiplied 3 with 3 which equals 9
Then I multiplied 9 with 4 which equals 36
Next I multiplied 36 with 5 which equals 180
Lastly I multiplied 180 with 6 which equals 1080

Then to check my answer I divided 1080 by 6
Then 180 by 5
Then 36 by 4
Then 9 by 3
Which equals 3!!



But it could also be 18, so I'm not sure!!

Answer 2

Work the problem backwards.
You ended with 3 mangoes after the 3rd prince ate half so he started with 6.
The second prince ate 1/3 and left 2/3 or 6. If 2/3x = 6, then 3/3x = 9
The first prince ate 1/4 and left 9. IF 3/4x = 9, then 4/4x = 12
The queen ate 1/5 and left 12. if 4/5x = 12, then 5/5x = 15
The King ate 1/6 and left 15. if 5/6x = 15, then 6/6x = 18
You started with 18 Mangos.

Answer 3

Calculate how many mangos were left each time. Reduce the number of mangos left by the fraction each person ate:
m=number of mangos
K ate (1/6)(m) leaving m-(1/6)m = (5/6)(m)
Q ate (1/5)(5/6)(m) = (1/6)(m) leaving m-(2/6)m= (2/3)m
P1 ate (1/4)(2/3)m=(1/6)m leaving m-(3/6)m=(1/2)m
P2 ate (1/3)(1/2)m=(1/6)m leaving m-(4/6)m = (1/3)m
P3 ate (1/2)(1/3)m=(1/6)m leaving m-(5/6)m=(1/6)m
After everyone ate there were (1/6)m left
(1/6)m = 3
m = 18
There were 18 mangos in the beginning

Answer 4

Originally there were x mangoes.

The king ate 1/6 leaving 5/6x left.
the queen ate 1/5 leaving 4/5 of 5/6 left
the prince_1 ate 1/4 leaving 3/4 of 4/5 of 5/6

now notice that the denominator of 3/4 is the same as the numerator of 4/5. The product of 3/4 4/5 and 5/6 is 3/6.
The third prince starts at 1/2 and it goes on.. the final equation is

x* 1/6 = 3

multiply both sides by 6 and you get
x = 18.

Now test it, just to be sure.
the king ate 1/6 or 3 leaving 15
the queen ate 1/5 or 3 leaving 12
the prince_1 ate 1/4 or 3 leaving 9
the prince_2 ate 1/3 or 3 leaving 6
the prince_3 ate 1/2 or 3 leaving 3

Its interesting that they ate the exact same ammount.

Note: they dont live on discworld because at night the fridges contents change in order to annoy midnight snackers.

Answer 5

there are six steps to your problem and since it starts with 1/6 it makes it easy. It goes form 1/6 to 1/5 to 1/4 to 1/3 to 1/2 to 1/1-- which is three. so it is all divided into sixths--meaning you need to find what three is 1/6 of. 1/6 of 18 =three. everyone got the same amount of mangoes on ecah trip--it works out that each took three. there were 18 to begin with. 1/6 of 18 is three leaving 15. 1/5 of 15 = three leaving 12. 1/4 of 12 is three, leaving 9, etc until 3 are left.

Answer 6

It's a trick question.

Everybody knows that servants don't like mangos.