2015 AMC 10A Problems/Problem 2

Problem

A box contains a collection of triangular and square tiles. There are tiles in the box, containing edges total. How many square tiles are there in the box?

$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}}\ 9\qquad\textbf{(E)}\ 11$ (Error compiling LaTeX. Unknown error_msg)

Solution

Let be the amount of triangular tiles and be the amount of square tiles.

Triangles have 3 edges and squares have 4 edges, so we have a system of equations.

We have tiles total, so .

We have edges total, so .

Solving gives, and , so the answer is .