Arianna's gain basis, given the adjusted basis of the personal residence can be found to be $311,985
How to find the gain basis ?
Arianna's gain basis is calculated based on the fair market value and the adjusted basis.
If the fair market value ($311,985) is less than the adjusted basis ($346,650), then her gain basis is equal to the fair market value.
In this case, her gain basis is $311,985. If the fair market value is greater than the adjusted basis, there is no loss basis because she has not incurred a loss on the property at the time of conversion.