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Yeah, hotels in Salt Lake are dirt cheap as long as you're not looking for anything beyond a bed (and since you're willing to sleep on the floor Ill go ahead and make that assumption).
I used to come out here on spring break and we'd pack 3-5 of us into the La Quinta or Best Western in Midvale/Sandy. Would come out to $20ish/person per night and they'd usually have some sort of free breakfast in the AM so you'd have that cost savings as well.