2015 AMC 10A Problem 2

Attempt Problem 2 of the 2015 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

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?

$3$

$5$

$7$

$9$

$11$

Answer: D

Concepts:system of equations

Difficulty rating: 870

Solution:

Let $x$ be the number of triangular tiles and $y$ be the number of square tiles. We then have that $x + y = 25$ and $3x + 4y = 84.$ Multiplying the first equation by $3$ gives us $3x + 3y = 75$ and subtracting this from the other equation gives us $y = 9.$

Thus, D is the correct answer.

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