Posted by **Xein** on Saturday, November 23, 2013 at 9:11am.

let s and w represent positive integers where x,y satisfy x/s+y/w=1 and s/x+w/y=4, find x+y in terms of s and w

It's really hard even for the teachers it took them a while. So I I was wondering how to solve it

- Math grade 9 and up -
**Jai**, Saturday, November 23, 2013 at 10:03am
x/s + y/w = 1

s/x + w/y = 4

You can use substitution.

From the first equation,

wx + sy = sw

x = (sw - sy)/w

Substitute to the second equation:

s/x + w/y = 4

sy + wx = 4xy

sy + (w)((sw - sy)/w) = 4((sw - sy)/w)y

sy + sw - sy = 4y(sw - sy)/w

sw^2 = 4swy - 4sy^2

4sy^2 - 4swy + sw^2 = 0

s(4y^2 - 4wy + w^2) = 0

Factoring,

s(2y - w)(2y - w) = 0

y = w/2

Substituting this to x:

y = w/2:

x = (sw - sy)/w

x = (sw - s(w/2))/w

x = (sw - sw/2)/w

x = (1/2)s

x = s/2

Thus, x + y = w/2 + s/2

Hope this helps :)

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