The relationship between the number of pencil sharpener a company can sell each week and the price of each sharpener p is given by the equation x = 2300 - 100 p At what price should the sharpeners be sold if the weekly revenue is to be $ 12000

The price p could be any of $8 or $15.

Step-by-step explanation:

The equation is a relationship between the numbers of pencil sharpener x can sell each week and the price of each sharpener p.

x = 2300 - 100p

xp = 12000

therefore,

x = 12000/p

insert the value of x in the equation

x = 2300 - 100p

12000/p = 2300 - 100p

12000/p + 100p - 2300 = 0

multiply through by p

12000 + 100p² - 2300p = 0

100p² - 2300p + 12000 = 0

divide through by 100

p² - 23 + 120 = 0

Find the number that we can multiply to give 120 and add to give - 23. The number are - 15 and - 8.

p² - 8p - 15p + 120 = 0

p (p - 8) - 15 (p - 8) = 0

(p - 8) (p - 15)

p = 8 or 15

x = 2300 - 100p

x = 2300 - 100 (8)

x = 2300 - 800

x = 1500 pencil sharpener sold

or

x = 2300 - 100 (15)

x = 2300 - 1500

x = 800 pencil sharpener sold

The price could be any of $8 or $15.