Kirchoff's law and circuit analysis

[fight_club_alum]

Homework Statement

23. In the figure, if I = 80 mA, determine the resistance R

Relevant Equations

Kirchoff's law

I assumed the current flows from the 20V so,
20V - 100 (i1) - Ri2 = 0
First loop
20V = 100i1 + Ri2

Second loop
+Ri2 + 40V - 200(0.08) = 0
Ri2 = -24

Back to equation 1

20 v = 100i1 + (-24)
therefore, i 1 = 0.44

For loop two:
i1 - i2 = i3
0.44 - i2 = 0.08
therefore i2 = 0.36 ohms

So, if R i2 = -24

R (0.36) = -24

R = -66.6666667 ohms
This is none of the choices and the answer key says d

Someone please help

 

[kuruman]

There is something wrong with the given numbers. I agree with your solution.

On edit: Actually this problem is a bit tricky. Try this: ignore the given 80 mA current and solve for the three currents as if they were unknown using symbols, e.g. $E_1$ for the 20 V battery, $2E_1$ for the 40 V battery, $R_1$ and $2R_1$ for the known resistors and $R$ for the unknown resistor. You will discover something peculiar about the current that flows through $R$. However, in view of this result, I don't see how one can get any of the listed choices.