$6\mathrm{.}12$ Sky Co$.$ sells state$-$of$-$the$-$art telescopes to individuals and organizations interested in studying the solar system.At December $31$ last year, the company's inventory amounted to $$250,000.$ During the first week of January this year, the company made only one purchase and one sale. These transactions were as follows:Jan. $2$ Sold one telescope costing $$105,000$ to Central State University for cash, $$140,000.$Jan. $5$ Purchased merchandise on account from LunarOptics, $$53,000.$ Terms, net $30$ days.a$.$ Prepare journal entries to record these transactions assuming that Sky Company uses the perpetual inventory system. Use separate entries to record the sales revenue and the cost of goods sold for the sale on January $2.$b$.$ Compute the balance of the Inventory account on January $7.$c$.$ Prepare journal entries to record the two transactions, assuming that Sky Company uses the periodic inventory system.d$.$ Compute the cost of goods sold for the first week of January assuming use of a periodic inventory system.e$.$ Which inventory system do you believe that a company such as Sky Company would probably use?