BTGmoderatorDC wrote:ACME's manufacturing costs for sets of horseshoes include a $11,450 initial outlay, and $19.75 per set. They can sell the sets $52.50. If profit is revenue from sales minus manufacturing costs, and the company produces & sells 987 sets of horseshoes, what was their profit?
(A) $20,874.25
(B) $30,943.25
(C) $41,308.50
(D) $51,817.50
(E) $53,624.25
Source: Magoosh

The alternative choices ARE far apart (except the last two ones), therefore we are allowed to use (always carefully!) approximations (to be reconsidered ONLY if we come close to $50,000) !!
$$? = {\rm{revenue}} - {\rm{costs}}\,\,\,\,\,\,\left( {{\rm{987}}\,\,{\rm{sets}}} \right)$$
$${\rm{revenue}} = 987\,\,sets\,\,\left( {{{\$ 52{1 \over 2}} \over {1\,\,{\rm{set}}}}} \right)\,\,\,\, \cong \,\,\,\$ 990 \cdot 52$$
$${\rm{costs}}\,\,\,{\rm{ = }}\,\,\,{\rm{11450 + }}987\,\,sets\,\,\left( {{{\$ 19{3 \over 4}} \over {1\,\,{\rm{set}}}}} \right)\,\,\,\, \cong \,\,\,\$ \left( {11450 + 990 \cdot 20} \right)$$
$$? \cong \,10 \cdot 99 \cdot \left( {52 - 20} \right) - 11450 \cong 10 \cdot 100 \cdot 32 - 11450 \cong 21000\,\,\left( \$ \right)$$


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

Regards,
fskilnik.