A very bright girl riding the Merry-Go-Round remarked, “A third of the number of children riding ahead of me, added to 3/4 of those riding behind me gives the correct number of kids on this ride”;

N = Total number of kids
Since this is a circle, the number of kids behind the girl = number of kids in front of her = N-1 as far as I understand.
(1/3+3/4)x(N-1)=N
N=13

X= Children ahead or behind her (its the same because its a circle)
1)1/3 X + 3/4 X = 13/12 X (she said this is the number of children in the merry go round)
So:2) X + 1 is also the number of children in the merry go round.. cause its everybody ahead or behind her plus her
(1)=(2)—> 13/ 12 X = X + 1—> X= 12 (the number of children in the merry go round)
Hope this time, I did not have any errors in the algebra :-/ X= Children ahead or behind her (its the same because its a circle)
1)1/3 X + 3/4 X = 13/12 X (she said this is the number of children in the merry go round)
So:2) X + 1 is also the number of children in the merry go round.. cause its everybody ahead or behind her plus her
(1)=(2)—> 13/ 12 X = X + 1—> X= 12 (the number of children in the merry go round)
Hope this time, I did not have any errors in the algebra ))<

As a merry-go-round is circular then there are the same number of kids riding ahead of the girl as there are behind her. This number is equal to the total number of kids on the ride minus one (the girl in the question):

13
As the riders are all in a circle, there are the same number in front of the bright girl as behind her. The only number that is divisble by 3 and also by 4 (to get 3/4) is 12 or a multiple of 12. One-third of this number plus 3/4 of this number must add up to one more than this number (to allow for the girl as well).
The only number that meets these criteria is 12 plus the girl, makes 13 altogether.
If there were thirteen altogether (including the bright girl) there would be 12 in front (one-third of 12 = 4) plus 12 behind (3/4 of 12 = 9) totalling 13 (9 + 4).

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Falwan| Profile May 11th, 2010 - 10:15 pm1/3 (x-1) + 3/4 (x-1) = x

x = 13

goofymushu| Profile May 12th, 2010 - 1:03 am12 including her

Hex| PUZZLE MASTER | Profile May 12th, 2010 - 4:46 amN = Total number of kids

Since this is a circle, the number of kids behind the girl = number of kids in front of her = N-1 as far as I understand.

(1/3+3/4)x(N-1)=N

N=13

engjs1960| Profile May 12th, 2010 - 8:46 amThere are 13 kids on the ride.

Shawn| PUZZLE GRANDMASTER | Profile May 12th, 2010 - 9:37 amAll of the other children on a merry-go-round are both ahead of AND behind a given observer.

x = total number of children, other than the little girl

We need to find x+1 = total number of children, including the little girl

1/3x + 3/4x = x + 1

x = 12

x + 1 = 13 = total number of children, including the little girl

suineg| PUZZLE MASTER | Profile May 12th, 2010 - 1:05 pmX= Children ahead or behind her (its the same because its a circle)

1)1/3 X + 3/4 X = 13/12 X (she said this is the number of children in the merry go round)

So:2) X + 1 is also the number of children in the merry go round.. cause its everybody ahead or behind her plus her

(1)=(2)—> 13/ 12 X = X + 1—> X= 12 (the number of children in the merry go round)

Hope this time, I did not have any errors in the algebra :-/ X= Children ahead or behind her (its the same because its a circle)

1)1/3 X + 3/4 X = 13/12 X (she said this is the number of children in the merry go round)

So:2) X + 1 is also the number of children in the merry go round.. cause its everybody ahead or behind her plus her

(1)=(2)—> 13/ 12 X = X + 1—> X= 12 (the number of children in the merry go round)

Hope this time, I did not have any errors in the algebra ))<

Hendy| Profile May 12th, 2010 - 2:22 pm1/3 of 12 = 4

3/4 of 12 = 9

4 + 9 = 13 total

12 (front or back) + 1 (bright girl) = 13

Blusummers13| Profile May 12th, 2010 - 6:25 pmThere are 13 riders.

suineg| PUZZLE MASTER | Profile May 12th, 2010 - 7:13 pm13 is the answer is X + 1= 12+1=13

cool man

munna| Profile May 13th, 2010 - 5:02 amTotal 13 riders including the girl.

Mashplum| PUZZLE MASTER | Profile May 13th, 2010 - 10:00 amn = # of other riders

3/4n + 1/3n = n + 1

9n + 4n = 12n + 12

13n = 12n + 12

n = 12

There were 13 riders.

Bobo The Bear| PUZZLE MASTER | Profile May 14th, 2010 - 10:16 amBecause the merry-go round is circular, every rider (other than the girl herself) is considered to be ahead of the girl AND behind the girl as well.

If there are “X” other riders, then the equation is:

(1/3)X + (3/4)X = X + 1

This yields a solution of X=12, and by including the girl, we have a total of 13 riders.

mimi112| Profile May 14th, 2010 - 11:14 am13 riders

jamesbuc| Profile May 14th, 2010 - 11:45 amAs a merry-go-round is circular then there are the same number of kids riding ahead of the girl as there are behind her. This number is equal to the total number of kids on the ride minus one (the girl in the question):

(x-1)/3 + 3(x-1)/4 = x

Multiply through by 12:

4(x-1) + 9(x-1) = 12x

13(x-1) = 12x

13x – 13 = 12x

x = 13

There are 13 children on the ride.

RK| Founder | Profile May 14th, 2010 - 12:21 pmvery good! 13 is correct

RogHyde| Profile November 10th, 2010 - 10:10 am13

As the riders are all in a circle, there are the same number in front of the bright girl as behind her. The only number that is divisble by 3 and also by 4 (to get 3/4) is 12 or a multiple of 12. One-third of this number plus 3/4 of this number must add up to one more than this number (to allow for the girl as well).

The only number that meets these criteria is 12 plus the girl, makes 13 altogether.

If there were thirteen altogether (including the bright girl) there would be 12 in front (one-third of 12 = 4) plus 12 behind (3/4 of 12 = 9) totalling 13 (9 + 4).