At the end of a certain year, the four organizations ranking $5$ through $8$ in home Internet users in the United States were eBay, the U$.$S$.$ Government, Amazon, and Lycos, with a combined audience of $112$ million users. Taking x to be the eBay audience in millions, y the U$.$S$.$ Government audience in millions, z the Amazon audience in millions, and u the Lycos audience in millions, it was observed that

y $$ z $=$ z $$ u

x $$ y $=3($y $$ u$)+9$

and x $$ y $+$ z $$ u $=16.$

How large was the audience of each of the four organizations at the end of that year?