You have just opened a new nightclub, Russ's Techno Pitstop, but you are unsure how much to charge for the cover charge (entrance fee). One week you charged $9 cover per guest and averaged 372 guests per night. The next week you charged $20 per guest and averaged 240 guests per night. Find the linear demand equation showing the number of guests q per night as a function of the cover charge p.
A) $q = - 12 p + 480$
B) $q = 12 p + 480$
C) $q = - 12 p + 492$
D) $q = - 12 p + 468$
E) $q = 12 p + 492$

Question

You have just opened a new nightclub, Russ's Techno Pitstop, but you are unsure how much to charge for the cover charge (entrance fee). One week you charged $9 cover per guest and averaged 372 guests per night. The next week you charged $20 per guest and averaged 240 guests per night. Find the linear demand equation showing the number of guests q per night as a function of the cover charge p.  
A) $q = - 12 p + 480$
B)  $q = 12 p + 480$
C)  $q = - 12 p + 492$
D)   $q = - 12 p + 468$
E)  $q = 12 p + 492$

Quizplus · Accepted Answer

The linear demand equation can be found by using the two given points: (9, 372) and (20, 240). The slope (m) is calculated as $\frac{240 - 372}{20 - 9} = \frac{-132}{11} = -12$. Using one of the points to solve for the y-intercept (b) in the equation $y = mx + b$, we get $372 = -12(9) + b$, leading to $b = 372 + 108 = 480$. Thus, the equation is $q = -12p + 480$.

You Have Just Opened a New Nightclub, Russ's Techno Pitstop q=−12p+480q = - 12 p + 480q=−12p+480

You Have Just Opened a New Nightclub, Russ's Techno Pitstop $q = - 12 p + 480$