positive integers
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sureshbala
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There's a nice explanation given by Ian.
Let's have a look from algebra point of view
We have
10[x/(x+y)+2y/(x+y)]=k
10[(x+2y)/(x+y)]=k
10[(x+y+y)/(x+y)]=k
10[(1 + y/(x+y)]=k
Given x<y
i.e x+y < 2y
i.e. x+y/y < 2
i.e. y/(x+y) > 1/2
So we have 1/2 < y/(x+y) < 1
Hence 10[(1 + y/(x+y)] must be in between 15 and 20.
So 18 is the possible answer
Let's have a look from algebra point of view
We have
10[x/(x+y)+2y/(x+y)]=k
10[(x+2y)/(x+y)]=k
10[(x+y+y)/(x+y)]=k
10[(1 + y/(x+y)]=k
Given x<y
i.e x+y < 2y
i.e. x+y/y < 2
i.e. y/(x+y) > 1/2
So we have 1/2 < y/(x+y) < 1
Hence 10[(1 + y/(x+y)] must be in between 15 and 20.
So 18 is the possible answer
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sureshbala
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Hi,navalpike wrote:Suresh, this is probably obvious to you but how did you go from :
10[(x+y+y)/(x+y)]=k
to
10[(1 + y/(x+y)]=k
Thanks,
We know that (a+b)/c = a/c + b/c
Similarly [(x+y)+y]/(x+y) = (x+y)/(x+y) + y/(x+y) = 1 + y/(x+y)
(consider a= x+y and b = y in the above example)
