Difference between revisions of "2015 AMC 10A Problems/Problem 2"
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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 12:35, 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 
.
