Difference between revisions of "2009 Grade 8 CEMC Gauss Problems/Problem 7"

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-==Problem==
+{{delete|page was moved}}
-The number of faces (<math>F</math>), vertices (<math>V</math>), and edges (<math>E</math>) of a polyhedron are related by the equation <math>F + V - E = 2</math>. If a polyhedron has <math>6</math> faces and <math>8</math> vertices, how many edges does it have?
-<math> \text{ (A) }\ 12 \qquad\text{ (B) }\ 14 \qquad\text{ (C) }\ 16 \qquad\text{ (D) }\ 18 \qquad\text{ (E) }\ 10 </math>
-==Solution 1==
-We can use the equation provided in the problem, and plug in <math>6</math> for <math>F</math>, and <math>8</math> for <math>V</math>:
-<math>6 + 8 - E = 2</math>
-We can combine <math>6</math> and <math>8</math> to get:
-<math>14 - E = 2
-Adding </math>E<math> to both sides, we get:
-</math>E + 2 = 14<math>
-Subtracting </math>2<math> from both sides of the equation, we get:
-</math>E = \boxed {\textbf {(A) } 12}<math>
-~anabel.disher
-==Solution 2==
-We can remember that a rectangular prism has </math>6<math> faces, </math>8<math> vertices, and </math>\boxed {\textbf {(A) } 12}$ edges, without doing any calculation.
-~anabel.disher