Why aren't these two ways of using bow-tie method yielding the same answer?

Question

If I have, 200 / (r+w) = 100 / (r-w), I solve this with:

200/(r+w) - 100 / (r-w) = 0

(200 (r-w) - 100 (r+w)) / (r^2-w^2)

It seems this is incorrect, but why?

I see the answer is actually to solve as: 200 (r-w) = 100 (r+w), but I'm not understanding when to use which, and why my first instinct is incorrect.

Thank you!

Answer 1

Hi Ann,

Your method isn't quite "wrong" per se. Let me copy and show you.

200/(r+w) - 100 / (r-w) = 0

(200 (r-w) - 100 (r+w)) / (r^2-w^2)

is what you provided... but you're mossing one key component.

The second line should actually be:

(200 (r-w) - 100 (r+w)) / (r^2-w^2) = 0

Now recall that you can multiply boht sides by (r^2-w^2) and get

200 (r-w) - 100 (r+w) = 0 ------> 200 (r-w) = 100 (r+w)

Now if I copy the answer you gave that the end...

200 (r-w) = 100 (r+w)

This is the same as what we got above.

Hope this help!

-Winn