Decals on LockersDate: 02/28/2002 at 21:39:18 From: Shemla Subject: Word problem Dear Dr Math, Can you please help me with this math problem? The lockers in Pythagoras Middle School are numbered 1 through 500. Starting the count with locker 1, every 6th locker has a blue decal, evey 9th locker has a yellow decal, and every 10th locker has a green decal. How many lockers have all three decals? Thank you. Date: 03/01/2002 at 14:24:34 From: Doctor Sarah Subject: Re: Word problem Hi Shemla - thanks for writing to Dr. Math. Let's start by drawing a chart. *'s will be lockers, B is for a blue decal, and Y is for a yellow decal. 18 36 54 *****B**** *B*****B** ***B*****B *****B**** *B*****B** ***B**** *B**** ********Y* *******Y** ******Y*** *****Y**** ****Y***** ***Y**** ****Y* We can see that there's a repeating pattern: at every third B decal there's also a Y decal on the same locker. These pairs occur at lockers 18, 36, 54... and these are numbers divisible by both 6 and 9. What numbers less than 500 are divisible by 6, 9, and 10? (Look for the least common multiple of those three numbers, and then multiples of that number less than 500.) Can you take it from here? - Doctor Sarah, The Math Forum http://mathforum.org/dr.math/ |
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