Circuit with Series and parallel resistors, voltage division rule

[qpham26]

Homework Statement

Given: The power absorbed by the 15 ohm resistor is 15 W. Find R.

http://sphotos-a.xx.fbcdn.net/hphotos-snc7/384382_495043340515186_1992745410_n.jpg

Homework Equations

parallel circuit for 2 resistor: R_eq =R₁R₂/ R₁+R₂

Voltage Division Rule: for series circuit V_R2 = V_sR₂/(R₁+R₂)

The Attempt at a Solution

P = V²/R
P = 15W, R = 15Ω
P at 15Ω = 15 W => V at 15Ω = 15V

=> V at R = 25V - 15V = 10V

So I go around the circuit from the left to right.

Start at the double 4Ω => R_eq = 2Ω
the 2Ω + 6Ω || 24Ω => R_eq = 6Ω
6Ω+4Ω || 15Ω => R_eq = 6Ω

now the circuit only have R and the 6Ω

apply V_R2 = V_sR₂/(R₁+R₂)
Plug in the number
solve for R = 4Ω

Please let me know if this is the right approach or if I have made a mistake.
Thanks for your time.

 

[CWatters]

Both the approach and the answer look ok to me.

 

[rude man]

answer is correct.