The Centerton Veterinarian Company starts the year with inventory costing $$360,000$ and ends the year with inventory costing $$400,000.$ During the period, purchases amounted to $$1,380,500.$ What was the average number of days required to sell an item of the company's inventory?

$89\mathrm{.}9$ days

$103\mathrm{.}5$ days

$38\mathrm{.}0$ days $\sqrt[\phantom{2}]{m}$

$140\mathrm{.}8$ days