2016 AMC 10B Problems/Problem 1: Difference between revisions

Revision as of 09:18, 21 February 2016

What is the value of $\frac{2a^{-1}+\frac{a^{-1}}{2}}{a}$ when $a= \frac{1}{2}$ ?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ \frac{5}{2}\qquad\textbf{(D)}\ 10\qquad\textbf{(E)}\ 20$

$\frac{frac{1}{a}*(2+frac{1}{2})}{a}$ then becomes $frac{frac{5}{2}}{a^{2}}$ which is equal to $frac{5}{2}*2^{2}$ = ${(D)}\ 10\qquad\textbf{(E)}\ 20$

Solution by ngeorge

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 ==Solution==
-<math>\frac{frac{1}{a}*(2+frac{1}{2})}{a}</math> then becomes <math>frac{frac{5}{2}}{a^{2}}</math> which is equal to <math>frac{5}{2]*2^{2}</math> = <math>{(D)}\ 10\qquad\textbf{(E)}\ 20</math>
+<math>\frac{frac{1}{a}*(2+frac{1}{2})}{a}</math> then becomes <math>frac{frac{5}{2}}{a^{2}}</math> which is equal to <math>frac{5}{2}*2^{2}</math> = <math>{(D)}\ 10\qquad\textbf{(E)}\ 20</math>
 Solution by ngeorge