Vita Water purchased a used machine for $$122,000$ on January $2,2023.$ It was repaired the next day at a cost of $$9,625$ and installed on a new platform that cost $$1,775.$ The company predicted that the machine would be used for six years and would then have a $$17,720$ residual value. Depreciation was to be charged on a straight$-$line basis to the nearest whole month. A full year$$s depreciation was recorded on December $31,2023.$ On September $30,2028,$ it was retired.

Required:

$1.$ Prepare journal entries to record the purchase of the machine, the cost of repairing it$,$ and the installation. Assume that cash was paid.