Alice owns land with an adjusted basis of $$510,000$ subject to a mortgage of $$250,000.$ On April $1,$ Alice sells her land subject to the mortgage for $$600,000$ in cash, $$500,000$ of marketable securities$,$ and property with a fair market value of $$100,000.$ Alice also paid a commission of $$8,000$ on the transaction. What is the amount realized?

Nora sold a piece of equipment to Adelyn on January $1,2024.$ Adelyn agreed to pay $$150,000$ for the equipment and assumed a $$5,000$ liability on the equipment. Nora incurred selling expenses of $$2,000$ on the sale.

Nora bought the equipment in $2022$ for $$180,000.$ Depreciation of $$69,000$ has been taken on the equipment. Nora performed routine maintenance on the equipment over the years of $$9,000$ and added a hydraulic lift to the equipment for $$12,000.$

a$)$ Compute the amount realized by Nora.

b$)$ Compute Nora's adjusted basis in the equipment.

c$)$ Compute Nora's realized gain or loss.