jmc

Let $C$ be the cost of carpeting a floor and $A$ be the area. By the definition of a direct proportion, we know that $C=kA$, where $k$ is a constant. Substituting $105$ for $C$ and $14\times 5=70$ for $A$, we can find that $k=3/2$. Then, the cost to carpet a floor that is $16\times 13$ square feet will be: $$\begin{array}{rl}C& =kA\\ & =(3/2)(16\times 13)\\ & =\boxed{312\text{ dollars}}.\end{array}$$