### Brain Teasers

# Carousel

Fred was in Washington, D.C., on a school trip to visit the Smithsonian. After lunch the teachers took the students to the Carousel on the Mall (this happened before they closed it down).

While Fred was enjoying his ride, he noticed that one-third of the number of his classmates riding ahead of him, plus three-fourths of them riding behind him, equaled the total number of students on the carousel.

How many students were riding the carousel?

While Fred was enjoying his ride, he noticed that one-third of the number of his classmates riding ahead of him, plus three-fourths of them riding behind him, equaled the total number of students on the carousel.

How many students were riding the carousel?

### Answer

13.The number of students ahead of him equals the number behind him. So,

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

When finding the common denominator for the left-hand side of the equation, we get 12, and the sum of the numerators then equals 13.

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## Comments

I got to 13 figuring all could be considered ahead and behind but I expected you would have one student next to Fred or something as a trick .. so, glad it was straight math

I thought it was pretty fun.

ummmmm thats wrong if u do 1/3 + 3/4 u have to change it to 4/12 + 9/12 and that equals 13/12 and that equals 1 and 1 /12

x=12 using that equation

how do you assume the number ahead= the number behind? Except possibly that on a carousel, all people are ahead and all people are behind you. Poor wording in the teaser.

You don't assume that the number ahead equals the number behind. You know it because a carousel is round.

I liked it pretty cool

At first glance, I thought it was impossible to solve.

Clever idea for a carousel!

Clever idea for a carousel!

Pretty cool. Gave me pause for a moment because I thought you weren't treating all in front as the same as all behind. Then I realized where the missing 1/12 was.

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