swerve wrote:What is the length in meters of a certain rectangular garden?
1) The length of the garden is 6 meters more than twice the width.
2) The length of the garden is 4 times the width.
Source: GMAT Paper Tests
All lengths are measured in meters.
\[? = L\,\]
\[\left( 1 \right)\,\,L = 2W + 6\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,W = 1\,\,\,\, \Rightarrow \,\,\,\,\,? = L\, = 8\,\, \hfill \\
\,{\text{Take}}\,\,W = 2\,\,\,\, \Rightarrow \,\,\,\,\,? = L\, = 10\,\, \hfill \\
\end{gathered} \right.\]
\[\left( 2 \right)\,\,L = 4W\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,W = 1\,\,\,\, \Rightarrow \,\,\,\,\,? = L\, = 4\,\, \hfill \\
\,{\text{Take}}\,\,W = 2\,\,\,\, \Rightarrow \,\,\,\,\,? = L\, = 8\,\, \hfill \\
\end{gathered} \right.\,\,\]
\[\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered}
\,L = 2W + 6\,\,\, \hfill \\
\,L = 4W \hfill \\
\end{gathered} \right.\,\,\, \Rightarrow \,\,\,\,\,\,2L = 4W + 12 = L + 12\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = L = 12\,\,\,\,\left[ {\,{\text{meters}}\,} \right]\,\,\,\,\,\]
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
