# 2015 AMC 10A Problems/Problem 2

Revision as of 11:42, 4 February 2015 by Warrenwangtennis (talk | contribs) (Created page with "==Problem== A box contains a collection of triangular and square tiles. There are <math>25</math> tiles in the box, containing <math>84</math> edges total. How many square tiles...")

## 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. ! Extra }, or forgotten $.)

## 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 .