A box contains a collection of triangular and square tiles. There are $25$ tiles in the box, containing $84$ edges total. How many square tiles are there in the box?
$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}\ 9\qquad\textbf{(E)}\ 11$
Let $a$ be the amount of triangular tiles and $b$ be the amount of square tiles.
Triangles have $3$ edges and squares have $4$ edges, so we have a system of equations.
We have $a + b$ tiles total, so $a + b = 25$.
We have $3a + 4b$ edges total, so $3a + 4b = 84$.
Multiplying the first equation by $3$ on both sides gives $3a + 3b = 3(25) = 75$.
Second equation minus the first equation gives $b = 9$, so the answer is $\boxed{\textbf{(D) }9}$.