To answer your question, if a radio states 50 watts audio output, then the actual power consumption will be somewhat higher, between 70 - 80 watts depending on what sort of circuitry the amplifier section uses.
As Bojcha says, keep the volume down. Most class A/B outputs use almost no power at low volume. The more you wind the volume up, the more power the system will use.
The only time a radio that can produce 50 watts will actually do so, is when the volume is up near maximum. How often do you listen to a radio like that? Not very often.
At moderate listening levels, the power amplifier section may be producing 5 - 10 watts, and consuming around 8 - 15 watts from the supply.
As mentioned above, you can use home stereo / radio systems that run off mains voltage, and drive them with an inverter, or you can go the other way and focus on 12 volt systems.
A lot of people who go off-grid choose to use 12 volt appliances and audio systems. You can go the easy way and use a car stereo (and associated amplifiers if required) or if you hunt around you can actually find radios and amplifiers that run on 12 volts.
An amplifier that can produce 50 watts per channel will not do it from 12 volts however, so amps this size generally have their own inverter built in to give +35/-35 volt rails or there abouts.