Suppose that cellphone cases are currently sold at $13.50. The following equation shows the number of cellphone cases sold 𝑥, in thousands, and the price, 𝑝: 100𝑥2 + 8𝑝2 = 2358

Question

If the price of cellphone cases are decreasing at $0.12 per week, find the rate of change of the sales.

Answer 1

12x^2 + 8p^2 = 2358

6x^2 + 4p^2 = 1179

x = sales in thousands

p= price = $13.50

each week they sell for 12 cents less

x1= sqr[1179 -4(13.5)^2]/6=sqr[393/2 - 2(182.25/3)]

following week

x2=sqr[1179- 4(13.38)^2]/6

rate of change in quantity per price= (x2-x1)/.12