ok here's the here's the problem
you have a circuit all elements are in series
voltage source E=20v
R1=2Kohms
R2=6Kohms
R3=x - drop in voltage across R3 is 4v

because you know the drop in voltage across R3=4v, you can determine the total drop in voltage across R1 and R2 must be 16V Right?
so from there u use the voltage divider rule to find out Rtotal using R1R2 = 8Kohms, Vx = 16v, E=20v...and you get Rt=10Kohms...Right?

so to find out R3 using voltage divider rule knowing Vx=4v,E=20v,and Rt=10kohms you get R3=2kohms right!?!?!

...the textbook gives the answer as 1.6k ohms, the answer i get is 2k ohms..
even if you try to solve the problem using the ratio method you still get 2 k ohms, but the book gives 1.6 k ohms...
WHAT GIVES!?!?!let me know if these words are too difficult to understand, i will try to simplify

 

I also get 2K as the value for R3.

I am not sure where the book came up with 1.6K.

hgmjr

 

It's 2k. Your textbook is wrong!