Difference between revisions of "2015 AMC 10A Problems/Problem 2"
(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...") |
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We have <math>3a + 4b</math> edges total, so <math>3a + 4b = 84</math>. | We have <math>3a + 4b</math> edges total, so <math>3a + 4b = 84</math>. | ||
− | Solving gives, <math>a = 16</math> and <math>b = 9</math>, so the answer is <math>\boxed{\textbf{(D)}9}</math>. | + | Solving gives, <math>a = 16</math> and <math>b = 9</math>, so the answer is <math>\boxed{\textbf{(D) }9}</math>. |
Revision as of 13:35, 4 February 2015
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. Unknown error_msg)
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
.