i am soo dumb lol, i am not getting it, your sketch is helping me out but i dont know how to get rp, rp is (r1*r2)/(r1+r2) but i dont have r values. I appreciate all of your help and deidcation
So the 120 + 30 = 150 volts is distributed across the voltage divider formed by 12 and Rp
such that 30/150 = Rp/(12+Rp)
This is an equation in Rp that you can solve to get Rp=3
Now substitute R and 3R for r1 and r2 in your parallel formula and equate to Rp =3
You now have an equation in R you can solve to get R = 4
Alternatively
In the bottom sketch note that the current divides in inverse proportion to the resistors so there is 3 times the current in the R resistor as in the 3R one.
thus total current is I plus 3I =4I
This must be = to the 10 amps incoming 4I = 10 > I = 2.5, 3I = 7.5
Since there is 30 volts across the single R resistor and 7.5 amps through it, Ohms law give R = 30/7.5 = 4 as before.
the secong way i got it, the cheat way but my problem is the algebra, solving that equation, and the r that i gave before was wrong i divided by the total v instead of the v going across
for part b i subtracted 1200w from the 12Ω from the total leaving me with 375. than i divided it by 4 leaving me 93.75 so r = 93.75 and r3 = 281.25 am i correct?