BTGmoderatorDC wrote:An appliance store purchases a radio for m dollars. The store then sells the same radio for n dollars. Was the appliance store's gross profit from the radio greater than twenty percent of its cost for the radio?
(1) m/n = 10/11
(2) n - m = 25
Source: Princeton Review
\[n - m\,\,\,\mathop > \limits^? \,\,\,\frac{1}{5}\left( m \right)\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,n\,\,\,\mathop > \limits^? \,\,\,\frac{6}{5}\left( m \right)\,\]
\[\left( 1 \right)\,\,\,\frac{m}{n} = \frac{{10}}{{11}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,n = \frac{{11}}{{10}}\left( m \right) = \frac{{5.5}}{5}\left( m \right)\,\,\,\mathop < \limits^{m\,\, > \,\,0} \,\,\,\frac{6}{5}\left( m \right)\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \]
\[\left( 2 \right)\,\,\,n = 25 + m\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {n,m} \right) = \left( {26,1} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\
\,{\text{Take}}\,\,\left( {n,m} \right) = \left( {525,500} \right)\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\
\end{gathered} \right.\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio. 
