Problem Solving

Manhattan Prep

Andrew sells vintage clothing at a flea market at which he pays $150 per day to rent a table plus $10 per hour to his assistant. He sells an average of $78 worth of clothes per hour. Assuming no other costs, which of the functions below best represents profit per day, P, in terms of hours, h, that the flea market table is open for business?

A. P(h) = 238 - 10h
B. P(h) = 72 - 10h
C. P(h) = 68h - 150
D. P(h) = 78h - 160
E. P(h) = -160h + 78

OA C

AAPL wrote:Manhattan Prep

Andrew sells vintage clothing at a flea market at which he pays $150 per day to rent a table plus $10 per hour to his assistant. He sells an average of $78 worth of clothes per hour. Assuming no other costs, which of the functions below best represents profit per day, P, in terms of hours, h, that the flea market table is open for business?

A. P(h) = 238 - 10h
B. P(h) = 72 - 10h
C. P(h) = 68h - 150
D. P(h) = 78h - 160
E. P(h) = -160h + 78

Let h=3.
Since an average of $78 is sold per hour, the total revenue for 3 hours = 3*78 = 234.
Since the cost for the day is composed of $150 for the table rental and $10 per hour for the assistant, the cost for the day = 150 + 3*10 = 180.
P = profit = revenue - cost = 234 - 180 = 54.

The correct answer must yield P=54 when h=3.
Only C works:
P = 68h - 150 = 68*3 - 150 = 204 -50 = 54.

The correct answer is C.

AAPL wrote:Manhattan Prep

Andrew sells vintage clothing at a flea market at which he pays $150 per day to rent a table plus $10 per hour to his assistant. He sells an average of $78 worth of clothes per hour. Assuming no other costs, which of the functions below best represents profit per day, P, in terms of hours, h, that the flea market table is open for business?

A. P(h) = 238 - 10h
B. P(h) = 72 - 10h
C. P(h) = 68h - 150
D. P(h) = 78h - 160
E. P(h) = -160h + 78

$$\left\{ \matrix{
\,{\rm{constant}} = {{\$ \,\,150} \over {1\,\,{\rm{day}}}} \hfill \cr
\,{\rm{variable}} = {{\$ \,\,10} \over {1\,\,{\rm{hour}}}} \hfill \cr} \right.$$

$$?\,\,\,\, = \,\,\,\,{\rm{profit}}\,\,{\rm{per}}\,\,{\rm{day}}\left( {\rm{h}} \right)\,\,\,\, = \,\,\,\,{{\left( {{\rm{revenue}} - {\rm{cost}}} \right)} \over {1\,\,{\rm{hour}}}}\,\, \cdot \,\,{\rm{h}}\,{\rm{hours}}\,\,\, - \,\,\,{\rm{constant}}\,\,\,\,\,\left[ \$ \right]$$

$$?\,\,:\,\,{{\$ \left( {78 - 10} \right)} \over {1\,\,{\rm{hour}}}} \cdot {\rm{h}}\,\,{\rm{hours}} - \$ 150\,\,\,\, \Rightarrow \,\,\,\,P\left( {\rm{h}} \right) = 68{\rm{h}} - 150\,\,\,\,\,\left[ \$ \right]$$


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

Regards,
Fabio.