jmc

Let $s$ be the number of stools in the room and $t$ be the number of tables. We are looking for the value of $t$. We can set up a system of equations to represent the given information, as follows:

$$\begin{array}{rl}s& =6t\\ 3s+4t& =484\end{array}$$To solve for $t$, we need to eliminate $s$ from the equations above. Substitute the first equation into the second to eliminate $s$, to get $3(6t)+4t=484$, or $t=22$. Thus, there are $\boxed{22}$ tables in the room.