Determine i_o using superposition.

First, kill the 10 volt and 8 Amp sources. I will use circuit reduction to find i_o.

The total resistance in series with the 45 volt source is 40 W, thus the current due to the 45 volt source is

i_o(45) = 45/40 = 9/8 A

Next, replace the 10 volt source and kill the 45 volt source. I will again use circuit reduction, this time involving a source transform.

The total resistance in series with the 5 volt source is 40 W, thus the current due to the 5 volt source is

io = - 5/40 = - 1/8 A

(Watch the sign)

Next, replace both voltage sources with wires, and reinsert the 8 amp source. I will use mesh analysis to determine io.

i2 = 8 A

Removing the 8 amp source leaves two meshes (0 and 1) around which to write KVL.

Mesh 0:

5 io + 40 (io - i1) + 15 (io - 8) = 0

60 io - 40 i1 = 120 (eq. 0)

Mesh 1:

10 i1 + 30 (i1 - 8) + 40 (i1 - io) = 0

- 40 io + 80 i1 = 240 (eq. 1)

Solving equations 0 and 1 yields

i0 = 6 A

Finally, adding all three results gives

i0 = 9/8 - 1/8 + 6 = 7 Amps.