As noted above, as soon as you make an unbalanced connection at one end of a wire, the whole thing becomes unbalanced. So for maximum noise immunity, you should use balancing adapters. This is the only way to run long mic cables to a boom or wired lav without risking noise pickup. For this situation, the best bet is to get a balanced interface for the computer. Run a very short cable from the source to the RCA jack, and as long a balanced XLR cable as you need to the pro equipment.
Similar interfaces are available to connect balanced sources to unbalanced equipment.
If you don't need balanced wiring and don't care about levels, start with the schemes below. It may cause problems with transformerless devices. If everything in your facility is unbalanced and the wires are fairly short, there's no point to using balancing adapters. Connect the other conductor to the sleeve of each plug. Use shrink wrap or tape to make sure the shield doesn't touch anything at the other end.