Problem Solving

swerve wrote:The sum of the ages of Doris and Fred is y years. If Doris is 12 years older than Fred, how many years old will Fred be y years from now, in terms of y?

A. y - 6
B. 2y - 6
C. y/2 - 6
D. 3y/2 - 6
E. 5y/2 - 6
Source: Official Guide

Now Algebra!!
\[?\,\,\,:\,\,\,\,F + y\,\, = \,\,f\left( y \right)\]
\[\left\{ \begin{gathered}
\left( 1 \right) \hfill \\
\left( 2 \right) \hfill \\
\end{gathered} \right.\begin{array}{*{20}{c}}
{\,D + F = y} \\
{\,D - 12 = F}
\end{array}\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,F + 12 = y - F\,\,\,\,\, \Rightarrow \,\,\,\,\,2F = y - 12\]
\[?\,\,\,:\,\,\,F + y\,\,\, = \,\,\,\left( {\frac{y}{2} - 6} \right) + y\,\,\, = \,\,\,\frac{{3y}}{2} - 6\]
This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.