Lucy had a general purpose truck (Old Truck) that she used in her sole proprietorship. Lucy originally acquired the Old Truck in 2020 by paying $27,600 in cash, performing consulting services for the seller worth $1,800, and financing the remainder of the purchase price with a $6,900 loan. During 2023, Lucy traded in the Old Truck to a car dealership while purchasing a used general purpose truck (Used Truck). Lucy and the car dealership are unrelated to each other. As part of the exchange, the dealership gave Lucy a trade-in allowance of $7,900 for the Old Truck (i.e., credited $7,900 against the total purchase price for the Used Truck) and assumed the remaining $3,400 outstanding balance of her liability (i.e., the unpaid balance of the $6,900 loan that Lucy took out when she acquired the Old Truck in 2020). After accounting for the trade-in allowance and assumed liability, Lucy still had to transfer $3,700 in cash to the dealership in order to pay for the Used Truck. Lucy properly took $27,936 of depreciation on the Old Truck. Finally, Lucy had to pay a $75 fee to transfer the Old Trucks title to the car dealership. The car dealership, which operates as a sole proprietorship, had acquired the Used Truck at an auction during 2022. The dealership paid $5,400 for the Used Truck, $330 as a fee to the auctioneer, and $1,900 to enhance the Used Truck during the process of getting it ready for sale. The car dealership uses a BSAD 169 Individual Taxation Page 3 Spring 2023 specific identification method for its used vehicles and paid its salesperson an $870 commission for the sale of the Used Truck to Lucy.

Required: Explain what amount, if any, Lucy and the car dealership must include in their respective gross incomes for 2023 from these transactions and what basis, if any, Lucy had in the Used Truck and the car dealership had in the Old Truck immediately after the transaction.

Please please explain step by step each concept and how you solved the requirement, the more in depth the better. I have been particularly struggling with the basis and adjusted basis.