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
.