AAPL wrote:Princeton Review
A father distributed his total wealth to his two sons. How much wealth did the father have?
1) The elder son received 3/5 of the wealth.
2) The younger son received $30,000.
All numbers are in thousands of dollars.
$$? = W$$
$$\left( {Y\, = \,\,{\text{younger}}\,\,{\text{part}}\,\,{\text{,}}\,\,\,E = {\text{elder}}\,\,{\text{part}}} \right)$$
$$\left( 1 \right)\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,\left( {Y,E} \right)\, = \left( {30,45} \right)\,\,\,\,\, \Rightarrow \,\,\,\,? = 75\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {Y,E} \right)\, = \left( {20,30} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 50\,\, \hfill \cr} \right.$$
$$\left( 2 \right)\,\,\left\{ \matrix{
\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {Y,E} \right)\, = \left( {30,45} \right)\,\,\,\,\, \Rightarrow \,\,\,? = 75\,\, \hfill \cr
\,{\rm{Take}}\,\,\left( {Y,E} \right)\, = \left( {30,40} \right)\,\,\,\,\, \Rightarrow \,\,\,? = 70\,\, \hfill \cr} \right.\,$$
$$\left( {1 + 2} \right)\,\,\,30 = Y = \frac{2}{5}\left( W \right)\,\,\,\,\, \Rightarrow \,\,\,\,? = W = 75$$
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
