SOLUTION: Two distinct integers, m and n, are chosen from the set {1, 2, 3, 4, … , 2009}. What is the maximum possible value of (2m + n) ÷ (m – 2n)?

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: Two distinct integers, m and n, are chosen from the set {1, 2, 3, 4, … , 2009}. What is the maximum possible value of (2m + n) ÷ (m – 2n)?      Log On


   

Question 316802: Two distinct integers, m and n, are chosen from the set {1, 2, 3, 4, … , 2009}. What is the maximum possible value of (2m + n) ÷ (m – 2n)?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
For the largest value of a fraction, choose the maximum value for the numerator divided by the minimum value for the denominator.
If the denominator was zero, the value of the fraction would be infinite.
In that case,
m-2n=0
m=2n
Since the maximum value m can take on is 2009.
Let's use the closest value to m%2F2 which would be n=1004.
m-2n=1
2m%2Bn=5022
%282m%2Bn%29%2F%28m-2n%29=5022 when m=2009 and n=1004