Question

A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-time fixed costs will total $18,813 and the variable costs will be $25 per book. With the other method, the one-time fixed costs will total \$64.408 , and the variable costs will be 11.25 per book. For how many books produced will the costs from the two methods be the same?

Answer 1

Production cost: y

Number of books: x

First method:

the one-time fixed costs will total $18,813 and the variable costs will be $25 per book

`y=18813+25x`

Second method:

the one-time fixed costs will total \$64.408 , and the variable costs will be 11.25 per book

`y=64408+11.25x`

For how many books produced will the costs from the two methods be the same?

Equal the funtions (equal the production cost of both methods) and solve to find x (number of books):

`\begin{gathered} 18813+25x=64408+11.25x \\ \\ \text{Subtract 18813 in both sides of the equation:} \\ 18813+25x-18813=64408+11.25x-18813 \\ 25x=11.25x+45595 \\ \\ \text{Subtract 11.25x in both sides of the equation:} \\ 25x-11.25x=11.25x+45595-11.25x \\ 13.75x=45595 \\ \\ \text{Divide both sides of the equation into 13.75:} \\ (13.75)/(13.75)x=(45595)/(13.75) \\ \\ x=3316 \end{gathered}`Then, the corst from the two methods is the same with 3316 books produced