Sale of Second Home jointly owned with Mother and Brother

In 2015, my mother purchased a condo for $84,900.  Along with my mother, my brother and I were also named on the deed, even though neither my brother nor I spent any money on the purchase and it was not our primary home.  The $84,900 was entirely my mother's money.  My mother died in 2024 and her name was taken off the deed, so the condo was now jointly owned 50:50 between me and my brother.  It is still a second home since my brother and I both have other primary residences.  When we sold it last November we got $180,000, so split 50:50 and after subtracting $15,000 in tax, title and agent fees, I got a check for $82,500 and my brother got $82,500.

Do I still claim this second home as a purchase, even though my brother and I never spent any money on the original purchase, or is it a gift, or "something else"?  Would the Proceeds be 50% of the final sale price ($90,000), or the $82,500 I actually received a check for?  And would the purchase price be $28,300.00, which is 1/3 of my mother's $84,900 purchase since the deed showed 3-way ownership at the time of purchase?