Proportion

Quote:

Originally Posted by Cyloc

Hey, - I'm taking Geometry as a course, and since we've just done doing proportions, I think it's the most accurate forum to post my question, which I could not find by searching; - however, I stuck on a problem that confuses me everytime I have to look on the question, - a proportion that looks like this:

Attachment 20109

I know that I need to cross multiply and all the good stuff, (I've been hearing this more than 2 times now), - i just need help on the steps doing it with the nice and cool n's.

Regards

$\displaystyle\frac{n-2}{2n}=\frac{n+4}{2n+5}\Rightarrow\ \left[\frac{2n+5}{2n+5}\right]\;\left[\frac{n-2}{2n}\right]=\left[\frac{2n}{2n}\right]\;\left[\frac{n+4}{2n+5}\right]$

$\displaystyle\Rightarrow\frac{2n^2-4n+5n-10}{(2n+5)(2n)}=\frac{2n^2+8n}{(2n)(2n+5)}$

$\displaystyle\ 2n^2+n-10=2n^2+8n\Rightarrow\ n-10=8n\Rightarrow\ 7n=-10$