Question

After 12 weeks, how much more will he made in sales of buttered popcorn than the sales of caramel popcorn

Answer 1

We have two functions for the sales of popcorn:

`\begin{gathered} B(w)=8w+9 \\ C(w)=6w-1 \end{gathered}`

being B(w) the number of buttered popcorn sold over "w" weeks and C(w) the number of caramel popcorn sold over "w" weeks.

We now have to calculate how much more he would have made after 12 weeks in sales of buttered popcorn than the sales of caramel popcorn.

We can calculate this as the difference of sales of buttered popcorn and the sales of caramel popcorn for w = 12.

Each sale will be the product of the cost per unit (in this case, is $11 for both types) and the number of units sold (B(w) or C(w), depending on the ytpe of popcorn).

Then, we can calculate the difference in sales as:

`\begin{gathered} D=11\cdot B(12)-11\cdot C(12) \\ D=11\cdot(8\cdot12+9)-11\cdot(6\cdot12-1) \\ D=11\cdot(96+9)-11\cdot(72-1) \\ D=11\cdot105-11\cdot71 \\ D=1155-781 \\ D=374 \end{gathered}`

Answer: he would have made $374 more in sales from buttered popcorn than from caramel popcorn.