A local retailer has determined that the number x of PortaBoy game systems sold in a week is related to the price p in dollars of each system.

Question

A local retailer has determined that the number x of PortaBoy game systems sold in a week is related to the price p in dollars of each system. 20 game systems were sold when the price was $120. When the systems went on sale the following week, 50 systems were sold at $75 a piece.

A. Find a linear function which fits this data. Use the weekly sales x as the independent variable and the price p as the dependent variable.

(b) Find a suitable applied domain:

(c) If the retailer wants to sell 80 PortaBoys next week, what should the price be?

Answer 1

(20, 120) and (50,75) are two points on a line with slope = (120-75)/(20-50)= 45/-30 = -3/2 = (P-120)/(x-20)

P-120 = (-3/2)(x-20) = (-3/2)x + 30

P= (-3/2)x + 150

-3x/2 = -150

x = (2/3)150 = 100 maximum at zero price

P(80) = (-3/2)80 + 150 = -120+150 = 30

At price = $30, 80 will be sold

domain is 0 < x < 100

at price= $150, no one buys any

at price = $0, only 100 are "sold"

you'd have to pay people to take more than 100