Figuring taxes on Airbnb income

[Jeff Piscioniere]

Hello all and thank you in advance for any help and info you might offer.  My wife and I are new overnight vacation rental owners of a cabin in Gatlinburg, TN.  We just closed out our first month of rental (June) and I need to pay my taxes to both the state and the local municipality.  Airbnb does not allow for adding a tax rate to the property's listing (unless I'm missing something, please enlighten me!).  I owe a combined 12.75%.  Technically in my booking rate/fees the taxes are added in.  Now I need to figure out how to back track on my income to figure what it would be if the 12.75% were not added in.  Example: $1000 ending deposit for the month; what is the income before the 12.75% which should have been charged to the guest be...$870-890 approx. range???  I actually figured an equation to get it where X is the amount I'm looking for:

X + (X * .1275) = $1000