Problem Solving

zachlebo wrote:A certain grocery purchased x pounds of produce for p dollars per pound. if y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

A) (x-y)s-xp
B) (x-y)p-ys
C) (s-p)y-xp
D) xp-ys
E) (x-y)(s-p)

is attacking this problem using smart numbers easier than algebra?

A

zachlebo wrote:A certain grocery purchased x pounds of produce for p dollars per pound. if y pounds of the produce had to be discarded due to spoilage and the grocery sold the rest for s dollars per pound, which of the following represents the gross profit on the sale of the produce?

A) (x-y)s-xp
B) (x-y)p-ys
C) (s-p)y-xp
D) xp-ys
E) (x-y)(s-p) /quote]

The cost to the grocery was xp dollars. Since y pounds were discarded, x - y was actually sold at a price of s dollars, and thus the revenue earned was s(x - y) dollars.

Thus, the gross profit was s(x - y) - xp dollars.

Answer: A