Question

25) A cereal company finds that if it spends $40,000 on advertising, then 100,000 boxes of cereal will be sold, and of it spends $60,000, then 200,000 boxes will be sold. How much advertising is needed to sell 1,000,000 boxes of cereal? *

Answer 1

We can find the rate of change of cereal sold to amount spent.

From given information,

Increase in boxes of cereal sold is 200,000 - 100,000 = 100,000

Increase in money spent is 60,000 - 40,000 = 20,000

The rate of change of boxes of celear sold to amount spent is:

100,000/20,000 = 5

If we were to write a linear equation of the form y = mx + b, this rate of change would be m.

Thus,

y = 5x + b

Keep in mind, x is amount spent and y is boxes of cereal sold

We need to find b, so we can easily put the point x = 40,000 and y = 100,000 to find b. Shown below:

y = 5x + b

100,000 = 5(40,000) + b

100,000 = 200,000 + b

b = -100,000

Final Equation of the Line:

`y=5x-100,000`

We need amount of money needed (x) for 1,000,000 boxes of cereal sold (y).

We can substitute and find the answer:

`\begin{gathered} y=5x-100,000 \\ 1,000,000=5x-100,000 \\ 5x=1,100,000 \\ x=220,000 \end{gathered}`

The third answer choice is correct.

$220,000