Braingle: 'Carousel' Brain Teaser

Carousel

Math brain teasers require computations to solve.

Puzzle ID:	#22919
Fun:	(2.22)
Difficulty:	(2.02)
Category:	Math
Submitted By:	phrebh
Corrected By:	phrebh

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?

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

darthforman May 15, 2005
zonahobo May 16, 2005	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
Cheerleader_09 May 26, 2005	I thought it was pretty fun.
Yoyobug02 Jun 08, 2005	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
Beaker Jun 17, 2005	x=12 using that equation
paul726 Dec 08, 2005	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.
phrebh Dec 08, 2005	You don't assume that the number ahead equals the number behind. You know it because a carousel is round.
shadowwerss Jul 03, 2006	I liked it pretty cool
pating Sep 11, 2007	At first glance, I thought it was impossible to solve. Clever idea for a carousel!
javaguru Feb 09, 2009	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.