Question

A small publishing company is planning to publish a new book. the production cost will include one-time fix costs (such as editing) and variable costs (such as printing). There are two production methods it could use. With one method, the one-timed fixed costs will total $15,756, and the variable costs will be $23.50 per book. With the other method, the one-timed costs will total $48,108, and the variable costs will be $12 per book. For how many books produced will the costs from the two methods be the same?

Answer 1

What we must do is equal both equations like this:

`15756+23.5\cdot x=48108+12\cdot x`

solving for x (numbers of books):

`\begin{gathered} 23.5\cdot x-12\cdot x=48108-15756 \\ 11.5\cdot x=32352 \\ x=(32352)/(11.5) \\ x=2813.2=2813 \end{gathered}`

In aproximately 2813 books