Fractions and School Enrollments
Date: 02/26/2003 at 21:34:20 From: Leontia Subject: Fractions The sum of 1/2, 1/3, and 1/4 of the enrollment of the Business School is exactly the enrollment of the Language School. The sum of 1/5, 1/6, 1/7, and 1/8 of the enrollment of the Business School is exactly that of the Design School. What are the enrollments of these three schools, assuming no school has more than 1000 pupils?
Date: 02/27/2003 at 10:23:58 From: Doctor Ian Subject: Re: Fractions Hi Leontina, The first thing you can do is add the fractions. If I tell you that the sum of 1/2 and 1/4 of all Republicans support a particular policy, then you can conclude that 1/2 + 1/4 = 2/4 + 1/4 = 3/4 of all Republicans support it, right? Same thing here. So you want to add 1/2, 1/3, and 1/4 to find out what fraction of the enrollment of the Business School is equal to the enrollment of the Language School. That will give you an equation like 11/17 B = L where B stands for the enrollment of the Business School, L stands for the enrollment of the Language School, and 11/17 is a fraction that I just made up. If you do the same thing again for the Design School, you'll end up with a second equation that will look like 13/24 B = D Now, note that the enrollments must be integers. You can't enroll part of a student. If B and L are both going to be integers, then B had better be a multiple of 17. And if B and D are both going to be integers, then B had better be a multiple of 24. So B would have to be a multiple of both 17 and 24, which narrows things down considerably, doesn't it? Again, note that I made up these fractions. You have to get the real ones yourself, by adding the fractions in the problem. If you're not sure how to add fractions, take a look at these answers from the Dr. Math archives: Adding Fractions http://mathforum.org/library/drmath/view/60691.html http://mathforum.org/library/drmath/view/61948.html Is this enough to get started? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
Date: 02/27/2003 at 21:18:42 From: Leontia Subject: Thank you (Fractions) Dear Dr Math, Thanks a lot for helping to clear my doubts in Maths again. Thanks for taking the time to answer my question. Thank you!
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