How Do You Calculate Power Absorbed by a Resistor in a Circuit?

[homo-sapiens]

Homework Statement

Determine the power absorbed by the 15 ohms resistor, see circuit below.(the ix, i1, and i2 are things i added)
http://puu.sh/bQyEk/5f47888b03.png

2. Homework Equations
the KCL law
the KVL law
the ohm's law
power = voltage * current

The Attempt at a Solution

I calculated the whole resistance of the second branch first. then I found the relationship between current ix and current i since the voltage of a loop = zero. I then calculated the current using the KCL current law. i then found a relationship between current i1 and current i2. I calculated current i2 and used the power = resistance * current * current.
My answer is way off from the answer key, and I would like to know what I did wrong??

http://puu.sh/bQyK1/715544a6a1.png

 

[jz92wjaz]

Your approach looks good. It looks like you miscalculated ix = 36/51*(.425).

 

[homo-sapiens]

ops! that was a minor mistake on my part, but the answer is still not right with the answer key...
here is the answer key
http://puu.sh/bQDw6/e03756b3b0.jpg

 

[jz92wjaz]

The answer key is wrong. It comes up with v = -19 when solving for -2 - 2*v/6 = v/8.5 + v/6 + v/6, which is clearly incorrect (I calculate v = -2.55).

 

[homo-sapiens]

OH! thank you so much for clearing this up for me. aw, never thought the answer key would be wrong. I guess I should believe in my methods more often. thank you again.

 

[jz92wjaz]

You're welcome! It's always unnerving when the answer key is wrong, but it's nice when you can spot the mistake so you know for sure.