i need help with a math question its rlly long?

Question

a king took 1\6 of the mangoes in a bowl.....queen took 1\5 of the mangoes of what the king had left..... prince took 1\4 of the remaining mangoes.......second price took 1\3 of what was then left... finally the third prince took 1/2 of what was left leaveing only 3 mangoes left
what is the answer and how did u get it
please please please help me on it

Answer 1

This is the kind of problem that occurs on standardized tests...

To solve it you have to work backwards from the final value.

The bowl had 3 mangoes after prince 3 took 1/2. That means that 3 is 1/2 of the number in the bowl before prince 3 took his.
So before prince 3, there were 6 mangoes in the bowl.
You get that by dividing the number left by the fraction remaining after the the objects are taken. 1/2 were taken so 1 - 1/2 = 1/2 remained... so divide by 1/2

The bowl had 6 mangoes after prince 2 took 1/3. That means hat 6 is 2/3 of the number in the bowl before prince 2 took his.
So before prince 2, there were 9 mangoes in the bowl.
Again, you get that by dividing the number left by the fraction remaining after the the objects are taken. 1/3 were taken so 1 - 1/3 = 2/3 remained... so divide by 2/3.

The bowl had 9 mangoes after prince 1 took 1/4. That meanss that 9 is 3/4 of the number in the bowl before prince 1 took his.
So before prince 1 there were 12 mangoes.

The bowl had 12 mangoes after the queen took 1/5. That means that 12 is 4/5 of the number before the queen took hers.
So before the queen, there were 15 mangoes.

The bowl had 15 mangoes after the king took 1/6. That means that 15 = 5/6 of the number before the king took his. So before the king, there were 18 mangoes in the bowl.

Answer 2

This problem is all about multiplying fractions. First, the king took 1/6 of the mangoes. Now, there are 5/6 left. The queen took 1/5 of the remaining, or 1/5 X 5/6. This is 1/6. Then the first prince took 1/4 of the remaining, or 1/4 X 4/6. This is 1/6 too. Now there are 3/6 mangoes left. he second prince took 1/3 of this, or 1/3 X 3/6. This is also 1/6. The third prince took 1/2 of what was left, or 1/2 X 2/6. This is also 1/6. So EVERYONE GOT 1/6 OF THE MANGOES. All that is left is 1/6, and this equals 3. The whole thing has to be 3 divided by 1/6, which equals 18.

Answer 3

as complex as it sounds. The question can easily be solved if you tackle the problem backwards.......this is how you can.....
after many steps of people taking away mangoes in different fractions... the 3rd prince took half oh what was left leaving 3 mangoes. this implies that there were (3*2=6) mangoes before the prince took a share
moving another step further back....
these 6 mangoes are what that are left when the second prince took 1/3 rd the mangoes that were present at that instant. it means the part he left = 1-1/3=2/3 th part corresponds to the 6 mangoes.
so if we take the no of mangoes before the second prince took a share = x
then what we have is
2x/3 = 6 ===> x=9
applying same strategy once again to the previous step ...
here it is (1-1/4)= 3/4 th part that is = 9
==> 3y/4=9 ===> y=12(where y is the total mangoes just before the prince took a share.
now do the same for the queen..only difference being the fraction is now = 1-1\5 = 4\5 th part
===> 4Z/5 = 12 ===>z=15
one final time for the king taking 1/6 th fraction.
===> 5t/6 = 15 ===> t=18(t= total mangoes at the beginning)
hence our required answer is 18 mangoes.

Answer 4

Work backwards:

3rd prince took 1/2, leaving 1/2. So 1/2 is 3 and he must have started with 6.
2nd prince took 1/3, leaving 2/3. 2/3 = 6 so he must have started with 9 (6*3/2)
1st prince took 1/4, leaving 3/4. 3/4 = 9 so he must have started with 12 (9*4/3)
The queen took 1/5, leaving 4/5. 4/5 = 12 so she must have started with 15 (12*5/4)
The king took 1/6, leaving 5/6. 5/6 = 15 so he must have started with 18 (15*6/5)

If you look at the numbers, everyone took the same number of mangoes, but because there were less in the bowl as it went round each person took a bigger fraction of what was left.

Answer 5

3rd prince took 1/2, leaving 3, so he was looking at 6 to start.

2nd prince took 1/3, leaving 2/3, which was 6, so he was looking at 9 to start.

1st prince took 1/4, leaving 3/4, which was 9, so he started with 12.

queen took 1/5, leaving 4/5, which was 12, so she started with 15.

king took 1/6, leaving 5/6, which was 15, so he started with 18.

If your question was how many mangoes in the bowl at the beginning, it was 18. But you didn't actually ask a question.

Answer 6

all these kinds of problems you start with a variable that represents the value you are looking for

I assume that the question is, how many mangoes did we start with.

let m=mangoes in the bowl at the beginning

so, m-1/6 m would equal what is left after the king took
(m, original mangoes minus one-sixth of the original mangoes)

m- 1/6 m= m(1-1/6)=5/6m

this makes sense, after the king took out 1/6, whats left is 5/6

now the queen gets a bowl with 5/6m, and takes 1/5 of it

so, 5/6m-(1/5*5/6m) is how much is left then

5/6m-(1/5*5/6m)=5/6m(1-1/5)=5/6m*4/5=4/5*5/6m

after a little thought it is easy to see that the others will work similarly

1/2*2/3*4/5*5/6m will be how much is left at the end, and that we are told equals three

so,

1/2*2/3*3/4*4/5*5/6m=3
120/720m=3
1/6m=3
m=3*6=18

m=18

now you can go back and check it by doing each royal mango munch one after the other

good luck
math is power

better check my arithmetic

Answer 7

There were x mangoes in the bowl
After the king took his mangoes there were 5x/6 left
After the queen there were 4x/6 left
Then 3x/6...
Then 2x/6
Then x/6 = 3.
So x=18.

Answer 8

You work backwards. You start with 3. Multiply this by the denominator of the last number. Keep doing this with all the numbers. This will get you to 2160 Mangoes at the start.

Answer 9

these are the numbers that you are given

a-1/6a=b
b-1/5b=c
c-1/4c=e
e-1/3e=f
f-1/2f=3

so you start with the last one where you only have one variable
f-1/2f=3
you need to solve for f
f(1-1/2)=3 factor out f
f(1/2)=3 simplify
f=6 divide both sides by 1/2 (multiply by two)

then do the same thing for e-1/3e=f
except replace the f variable with the answer you just got (6)

you get f=9

do it again replacing e=9 and you get c=12

again with c=12, you get b=15

again with b=15 and you get a=18


AND THEREFORE THE ANSWER IS 18