2015 AMC 10A Problem 2

Below is the professionally curated solution for Problem 2 of the 2015 AMC 10A, 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.

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Concepts:system of equations

Difficulty rating: 870

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?

$3$

$5$

$7$

$9$

$11$

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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