Point E, F, G and H lie on a line that order. Ig EG=5/3EF and HF=5FG, then what is EF/HG?

Question

anonymous · Answer

T_T Somebody please help me... This kind of problem had showed up several time on my tests in class and I get them wrong every time.. I would really appreciate it.

anonymous · Answer

wait can you rewrite the values of each of the line segments seperately, I'm a bit confused

anonymous · Answer

of course!$$EG=\frac{ 5 }{ 3 }EF$$$$HF= 5FG$$ What is $$\frac{ EF }{ HG}$$

anonymous · Answer

Using the first equation, solve for EF. 
EG*(3/5)=(3/5)*(5/3)*EF
EG*(3/5)=EF

To find HG we can do HF-GF 
So HF = 5FG ,  FG = (1/5)HF
5FG-(1/5)(5FG)=5FG-FG = 4FG

Now, rewrite.. EF/HG = 
(EG*(3/5))/5FG

anonymous · Answer

Thank you!!! :D

anonymous · Answer

No prob!! :D