The following transactions and adjusting entries were completed by a paper$-$packaging company called Gravure Graphics International. The company uses straight$-$line depreciation for trucks and other vehicles, double$-$declining$-$balance depreciation for buildings, and straight$-$line amortization for patents.

January $2,2020$ Paid $$105,000$ cash to purchase storage shed components.

January $3,2020$ Paid $$4,000$ cash to have the storage shed erected. The storage shed has an estimated life of $10$ years and a residual value of $$7,000.$

April $1,2020$ Paid $$51,000$ cash to purchase a pickup truck for use in the business. The truck has an estimated useful life of five years and a residual value of $$5,000.$ This vehicle is to be recorded in the Truck account.

May $13,2020$ Paid $$900$ cash for minor repairs to the pickup truck's upholstery.

July $1,2020$ Paid $$10,000$ cash to purchase patent rights on a new paper bag manufacturing process. The patent is estimated to have a remaining useful life of five years.

December $31,2020$ Recorded depreciation and amortization on the pickup truck, storage shed, and patent.

June $30,2021$ Sold the pickup truck for $$43,000$ cash. $($Record the depreciation on the truck prior to recording its disposal.$)$

December $31,2021$ Recorded depreciation on the storage shed. Recorded the patent amortization. After recording the patent amortization, determined that the patent was impaired and wrote off its remaining book value $($i$.$e$.,$ wrote down the book value to zero$).$

Prepare the journal entries required on each of the above dates.