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2015 AMC 10A Problem 2

Problem 2 of 25EasierAlgebra

A box contains a collection of triangular and square tiles. There are 2525 tiles in the box, containing 8484 edges total. How many square tiles are there in the box?

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Solution

Let xx be the number of triangular tiles and yy be the number of square tiles. We then have that x+y=25 x + y = 25 and 3x+4y=84. 3x + 4y = 84. Multiplying the first equation by 33 gives us 3x+3y=75 3x + 3y = 75 and subtracting this from the other equation gives us y=9.y = 9. Thus, D is the correct answer.

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Concepts: system of equations

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.