Question

You have just opened a new dance club, Swing Haven, but are unsure of how high to set the cover charge (entrance fee). One week you charged $4 per guest and averaged 80 guests per night. The next week you charged $10 per guest and averaged 44 guests per night. (a) Find a linear demand equation showing the number of guests q per night as a function of the cover charge p.

Answer 1

`q = -6p + 104`

Explanation:

Linear function:

A linear function has the following format:

`q = mp + b`

In which m is the slope and b is the q-intercept.

One week you charged $4 per guest and averaged 80 guests per night. The next week you charged $10 per guest and averaged 44 guests per night.

This means that we have these following points: (4,80), (10,44).

Finding the slope:

With a pair of points, the slope is given by the change in q divided by the change in p.

Change in q: 44 - 80 = -36

Change in p: 10 - 4 = 6

Slope:
`m = (-36)/(6) = -6`

So

`q = -6p + b`

Finding b:

We replace one of the points. Replacing (4,80).

`q = -6p + b`

`80 = -6*4 + b`

`b = 104`

So

`q = -6p + 104`