Question

A cereal company finds that 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.

A) Write a linear equation that relates the money spent to boxes sold.
B) How much should this company spend on advertising to sell 385,000 boxes of cereal?

Answer 1

A) The linear equation that relates the money spent to boxes sold is y = 5x - 300. B) The company should spend $137,000 on advertising to sell 385,000 boxes of cereal.

Step-by-step explanation:

A) To write a linear equation that relates the money spent to boxes sold, we can use the point-slope form of a linear equation. Let x represent the money spent on advertising (in thousands of dollars) and y represent the number of boxes sold (in thousands). We have two points: (40, 100) and (60, 200). Using the formula (y - y1) = m(x - x1), where m is the slope, we can calculate the slope as follows:

m = (y2 - y1) / (x2 - x1) = (200 - 100) / (60 - 40) = 100 / 20 = 5

Now we can plug one of the points and the slope into the point-slope form: y - 100 = 5(x - 40)

Finally, simplify the equation to slope-intercept form: y = 5x - 300

B) To find the amount the company should spend on advertising to sell 385,000 boxes, we substitute y = 385 into the equation and solve for x:

385 = 5x - 300

5x = 685

x = 137

Therefore, the company should spend $137,000 on advertising to sell 385,000 boxes of cereal.