On January $2,2023,$ Direct Shoes Inc. disposed of a machine that cost $$102,000$ and had been depreciated $$56,050.$ Present the journal entries to record the disposal under each of the following unrelated assumptions:

a$.$ The machine was sold for $$45,500$ cash.

b$.$ The machine was traded in on new tools having a $$153,000$ cash price. A $$58,000$ trade$-$in allowance was received, and the balance was paid in cash. Since the tools have been customized, the fair values are not known.

c$.$ The machine plus $$86,000$ was exchanged for a delivery van having a fair value of $$122,000$

d$.$ The machine was traded for vacant land adjacent to the shop to be used as a parking lot. The land had a fair value of $$93,000,$ and Direct Shoes Inc. paid $$43,000$ cash in addition to giving the seller the machine.