help with a word problem Please

Question

Wayside Auto Sales discovers that when $1000 is spent on radio advertising, weekly sales increase by $101,000. When $1250 is spent on radio advertising, weekly sales increase by $126,000. Assuming that sales increase according to a linear equation, by what would sales increase when $1500 is spent on radio advertising?

Answer 1

The weekly sales depends on how much is invested into the company.  You have to spend money in order to make money as the saying goes.

 

Amount spent is independent variable

Weekly sales is dependent variable

 

Now, we need to convert the information into 2 coordinate points

 

Point 1 = (1000, 101)

Point 2 = (1250, 126)

 

Note that the y coordinate of each point is in the unit of thousands for easy calculating.

 

 

Since we assume a linear relationship, we need to find the slope of the line.

 

m = (126 - 101) / (1250 - 1000)

m = 25 / 250

m = 0.1

 

Next, use the point-slope form of the equation to get the equation of the relationship.

 

y - y₁ = m(x - x₁)

 

where:

m = slope

(x₁ , y₁) = Point 1

 

y - 101 = 0.1(x - 1000)

 

y = 0.1x - 100 + 101

 

 

y = 0.1x + 1

 

This is your function.

 

Now, we plug in x=1500 into this function to find the weekly sales increase at that investment.

 

y = 0.1(1500) + 1

 

y = 150 + 1

 

y = 151

 

 

Since the y value is in units of thousands, the weekly sales is $151,000.