Problem Solving

BTGmoderatorDC wrote:If a mixture of ground meat consists of 2 pounds of veal that costs x dollars per pound, and 5 pounds of beef that costs y dollars per pound, what is the cost, in dollars, per pound of the mixture?

(A) 2x + 5y
(B) (2x + 5y)/xy
(C) 5(2x + 5y)
(D) x + y
(E) (2x + 5y)/7

GMATGuruNY wrote:

BTGmoderatorDC wrote:If a mixture of ground meat consists of 2 pounds of veal that costs x dollars per pound, and 5 pounds of beef that costs y dollars per pound, what is the cost, in dollars, per pound of the mixture?

(A) 2x + 5y
(B) (2x + 5y)/xy
(C) 5(2x + 5y)
(D) x + y
(E) (2x + 5y)/7

Even in a trivial exercise like this one, we may (and should!) use the winning triad, beginning with its most important leg, our FOCUS:
$$? = {{{\rm{total}}\,\,{\rm{\$ }}} \over {{\rm{total}}\,\,{\rm{pounds}}}}$$
Now it´s time to connect it to DATA (second leg) as soon as possible:
$${\rm{total}}\,\,{\rm{pounds}} = 2 + 5 = 7\,\,\,\,\,\left[ {pound} \right]$$
$${\rm{total}}\,\,{\rm{\$ }}\,\,\, = \,\,\,2\,\,{\rm{pounds}}\,\,\left( {{{x\,\,\,\$ } \over {1\,\,{\rm{pound}}}}\matrix{
\nearrow \cr
\nearrow \cr

} } \right) + 5\,\,{\rm{pounds}}\,\,\left( {{{y\,\,\,\$ } \over {1\,\,{\rm{pound}}}}\matrix{
\nearrow \cr
\nearrow \cr

} } \right) = 2x + 5y\,\,\,\,\,\left[ \$ \right]$$
Obs.: arrows indicate licit converters.
$$? = {{2x + 5y} \over 7}$$
We found our expression among the alternative choices (third leg)... it´s done!

This solution follows the notations and rationale taught in the GMATH method.

Regards,
fskilnik.