Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Product Promotion Application

A cereal company finds that the number of people who will buy one of its products in the first month that the product is introduced is linearly related to the amount of money it spends on advertising. If it spends $40,000 on advertising, then 100,000 boxes of cereal will be sold and if it spends $60,000, then 200,000 boxes will be sold. Write a linear equation that relates the amount A spent on advertising to the number of x boxes the company aims to sell.

The answer is y = (1/5)x + 20,000.

I would like a step by step reply that will display how the equation was formed based on the information in the application.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,172

Re: Product Promotion Application

It says it is linear so y = mx + c again.

You can find enough information to get the coordinates of two points. Don't know the intercept this time.  But you can plug in those coords and solve the simultaneous equations for m and c.

Or find m from the two points and then plug in that m with one set of coords to get c.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Product Promotion Application

A cereal company finds that the number of people who will buy one of its products in the first month that the product is introduced is linearly related to the amount of money it spends on advertising. If it spends $40,000 on advertising, then 100,000 boxes of cereal will be sold and if it spends $60,000, then 200,000 boxes will be sold. Write a linear equation that relates the amount A spent on advertising to the number of x boxes the company aims to sell.

I would like a step by step reply that will display how the equation was formed based on the information in the application.

Last edited by amnkb (2023-11-22 03:00:05)

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Product Promotion Application

It says it is linear so y = mx + c again.

You can find enough information to get the coordinates of two points. Don't know the intercept this time.  But you can plug in those coords and solve the simultaneous equations for m and c.

Or find m from the two points and then plug in that m with one set of coords to get c.

Bob

I have no idea how to get 1/5, the coefficient of x.

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Product Promotion Application

A cereal company finds that the number of people who will buy one of its products in the first month that the product is introduced is linearly related to the amount of money it spends on advertising. If it spends $40,000 on advertising, then 100,000 boxes of cereal will be sold and if it spends $60,000, then 200,000 boxes will be sold. Write a linear equation that relates the amount A spent on advertising to the number of x boxes the company aims to sell.

I would like a step by step reply that will display how the equation was formed based on the information in the application.

What is the value of A_1 & A_2?

What is the value of x_1 & x_2?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,172

Re: Product Promotion Application

If it spends $40,000 on advertising, then 100,000 boxes of cereal will be sold and if it spends $60,000, then 200,000 boxes will be sold. Write a linear equation that relates the amount A spent on advertising to the number of x boxes the company aims to sell.

So x is for the boxes so y must be for the costs. => (100000 , 40000) and (200000 , 60000) are points on the line.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Product Promotion Application

Two points leads to finding the slope. We then use the point-slope formula
amnkb found.