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Wow, I think you are asking for a lot of today's battery technology.
Any battery that can run an inverter to pump out much amperage at 120 volts will have to be huge and heavy. Lights and a stereo can eat up a battery fast.
It sounds like they need a small Honda generator and those are a lot more than your budget.
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Glen
50 Year member of the Porsche Club of America
1985 911 Carrera; 2017 Macan
1986 El Camino with Fuel Injected 350 Crate Engine
My Motto: I will never be too old to have a happy childhood!
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