I respectfully disagree. My listening room is 18' x 20', but extends into an eating room and kitchen. Total area is 18' x 32'. My Polks (not even their top of the line) fill that space and more. You need a powerful subwoofer, like one of the better SV Subwoofer models to get bass in an area that large. Your budget is fine with the models suggested above. I would try to get into two front towers with at least dual 8" drivers though. You don't want a hole in your bass if you like jazz, trying to find the frequencies between your sub and 6" woofers. They may say they go down to 35hz, but they won't keep up with a powerful sub in a room your size. Very important with jazz, which I have a large collection.
