Introduce yourself as the new owner, say you want to assure them that you are going to honor their leases at the current rate but that the cost of financing and maintaining the building dictates rents be raised to market rates at the end of their leases.

The applicant doesn't dictate the terms of your application and lease -- that's up to you.

The drawback is that increasing the rent comes with red-tape and the possibility that the rent will actually be LOWERED, if the market dictates it's too high. 

Be prepared to file the eviction within 3 days of the lease's expiration date (or whatever your lease and state laws dictate), and do not accept any money from her after the eviction is filed. 

Fair housing does not dictate that landlords do not have the right to choose based on qualifications. 

@John HodsonYou might let the market dictate what you do.

Generally, we choose the first qualified candidate, but the point is I don't have someone dictating my business practices.

The size of the unit and the area dictates the tenant pool.

She previously asked some landlords and got mixed answers, from "what's it to you, you're the tenant, it's not your place to dictate to the landlord" to "that guy can get in trouble...the law..."  

Mom/dad gets a place to live in their golden years, which is something you might have needed to pay for any-damn-ways except this way it isn't one of those abusive dictator nurse places, and X years from now your reward is that you have a new rental property that you only had to put 5% down on.