Write an equation that relates the amount A spent on advertising to the number x of boxes the company aims to sell.

Question

A cereal company finds that the number of people who will buy one of its products in the first month that it is introduced is linearly related to the amount of money it spends on advertising. If it spends $80,000 on advertising, then 100,000 boxes of cereal will be sold, and if it spends $90,000 on advertising, then 200,000 boxes of cereal will be sold. Write an equation that relates the amount A spent on advertising to the number x of boxes the company aims to sell.

Answer 1

x = number of boxes to be sold

A = amount spent on advertising at level x

 

(100000, 80000) and (200000, 90000) are two points on the line

 

slope = (90000-80000)/(200000-100000) = 1/10

 

Equation of line:  A - 80,000 = (1/10)(x - 100,000)

 

                              A - 80,000 = (1/10)x - 10,000

 

                                              A = (1/10)x + 70,000