How do you find good tenants in Chicago?

[Robert Andersen]

Recently posted a 3 bedroom completely renovated apartment on Zillow, Craigslist, Domu and Apartments.com. The apartment is in a good area of Chicago.I've gotten nothing but awful applicants despite being very clear in the description of the property that I'm going to be doing a background check and not accepting tenants with prior evictions or bad credit. 

Rent is listed at 1700 and I keep getting applicants with a combined income and three kids making 38k/48k. The numbers don't work. You can't afford 1700 a month making 38k with three kids and a car payment. 

The listings been up for 15 days and I've gotten close to 100 messages combined from all the platforms listed. Out of those 100 maybe 15 turned into showings and out of that 15 two took an application then never filled it out. 

I'm also getting a lot of section 8 applicants that are very militant with wanting to move in right away. I've had them make threats against me when I tell them I'm going to be doing a background check. 

How do I avoid all this mess?