Katie is assessing the inventory of office chairs. Currently there are $9$ model A chairs in stock that are priced at $$289\mathrm{.}13$; $9$ model B chairs in stock that are priced at $$254\mathrm{.}05$; and $7$ model C chairs that are priced at $$176\mathrm{.}51.$ Michael wants to know the average cost per chair of the inventory at the current moment. Katie calculates the average cost per chair to be:

Round your final answer to the nearest cent $[2$ decimals$]$ with the appropriate units.