What to do when you get too much interest in a Unit?

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I just listed a 1 Bedroom in my Triplex and I got a tremendous response in less than 24 hours from posting, but a lot of it is junk. Here are the stats.

Listed Price: $850 / Mo

Market Range: $800 - $975 / Mo

My Unit: Above Average compared to market

And, here are the results so far:

Inquires to rent: 48 (in under 24 hours)

Showings Held: 8 (So far, more scheduled)

Applications 3 (So far)

The only problem is all of the people that applied so far have credit under 650 and the person above 650 has an income of 2.7x of rent. Looking for any advice or feedback on how to best handle the situation.