Use the node-voltage method to find how much power the current source extracts from the circuit if i=7.8 A and v = 35 V. Answer in watts.?

Parallel combo of r's is 4.545ohms

I(v)=-6.455A.  V(50)=67.273v

P(i)=67.273v*7.8A=524.7W

Circuit simulator applet 

This ckt only has one "Node" above the 50Ω since the 1Ω and 4Ω are in series.

Let the bottom left of the ckt = ground and above the 50Ω be node V1

KCL at V1:

-7.8 + V1/50 + (V1-35)/5 = 0    Multiply eq. by 50

-390 + V1 + 10V1 - 350 = 0

11V1 = 350+390 = 740  so V1 = 750/11

The current source delivers 740/11 * 7.8 = 5772/11 W = 524.73W

The voltage source consumes 35V * 355/55 A = 225.91W

The resistance consumes (74/55)²*50+(355/55)²*5 = 298.82W

Total consumed = 225.91+298.82 = 524.73W  Checks