2015 AMC 10A Problems/Problem 2

Revision as of 12:35, 4 February 2015 by Warrenwangtennis (talk | contribs) (Solution)

Problem

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?

$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}}\ 9\qquad\textbf{(E)}\ 11$ (Error compiling LaTeX. ! Extra }, or forgotten $.)


Solution

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 $3a + 4b = 84$.

Solving gives, $a = 16$ and $b = 9$, so the answer is $\boxed{\textbf{(D) }9}$.

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