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i really think 20W is underpowered for a crowd of up to 200 especially since i bet that's is peak power rating. the sound would distort before you got any decent volume out of it.
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$200 is not reasonable for something that will work decently.
You're looking at about $100-150 on a decent wireless mic alone (used, on ebay)
The PA system should be at least 2x100 watts, I think.
So, speakers, a mixer and amp, or a powered mixer, and cables... $200 isn't very realistic.
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Peavey has a few compact, low end systems that might be closer to your budget. since it's for speaking, sound quality (beyond not distorting out) shouldn't be too much of a factor. you're probably going to have to let go of the wireless part if you don't have much of a budget.
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the thing you linked to will sound like crap. go to RS and buy a wired $40 mic and then get a cheap-o PA and plug it in and be happy, probably for about $200.
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if you wanted a 1 piece solution, this is from Mackie and has more power:
this is the Peavey system i mentioned. i've worked with this (guitar/vocal) in a medium sized room and was surprised by its capabilities (though i'd never use it for my needs by choice.)
Peavey also has another system that's even smaller that zzounds carries but i haven't worked with it.
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On a whim, I picked up a wireless (lavalier) mic from DAK for $50. Bottom line, it works just fine. Around 50W of "RMS" amp power will meet your needs with a fairly efficient speaker, i.e. one with a sensitivity rating of 92dB/W/m or better. I say this as a professional loudspeaker designer and former commercial sound guy. You can way over-buy on power and quality for simple voice reproduction, where you are re-enforcing the voice rather than replacing it....
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I've got some experience with this sort of stuff. I also have a cheapie wireless mic ($20?) that works just fine too. Solid opinions above, you would need two of the amps you linked to to start to be of any use with 100 people.
I would increase the budget to $200 for starters.
Doesn't like, everyone have an unused guitar amp in their basement?