zz0vlb wrote:
A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $37500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?
A. 5
B. 6
C. 9
D. 10
E. 15
\(\left. \matrix{\\
A\,\,:\,\,\,\$ 125 \cdot 10\,\, \hfill \cr \\
B:\,\,\,\$ 250 \cdot 10 \hfill \cr \\
C:\,\,\,\$ 400 \cdot 10\, \hfill \cr} \right\}\,\,\,{\rm{each}}\)
\(A:B:C = 6:2:1\,\,\,\left( {{\rm{quantities}}} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{\\
A = 6k \hfill \cr \\
B = 2k \hfill \cr \\
C = k \hfill \cr} \right.\,\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)\)
\(? = k\)
\(6k\,\,\,A\,\,{\rm{units}}\,\, \cdot \,\,\left( {{{\$ 125 \cdot 10} \over {1\,\,A\,\,{\rm{unit}}}}\,\,\matrix{\\
\nearrow \cr \\
\nearrow \cr \\
\\
} } \right)\,\,\,\,\,\, = \,\,\,\,\,\$ \,3750 \cdot 10\,\,\,\,\)
Obs.: arrows indicate
licit converter (UNITS CONTROL technique).
\(? = k = \frac{{3750}}{{6 \cdot 125}} = \underleftrightarrow {\frac{{3750}}{{3 \cdot 250}} = \frac{{375}}{{3 \cdot 25}}} = \frac{{125}}{{25}} = 5\)
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.