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$65,054, and the variable costs will be$8.25per book. With the other method, the one-time fixed costs will total$12,539, and the variable costs will be$19.50per book. For how many books produced will the costs from the two methods be the same?

The number of books produced at which the costs from the two methods be the same is 4668 books

Step-by-step explanation:

Here, we have

For the first production method

Fixed cost = $65,054 and variable cost per book = $8.25

For the second production method

Fixed cost = $12,539 and variable cost per book = $19.50

Therefore, let the number of books at which the to methods cost the same be M, we then have

$65,054 + $8.25 × M =  $12,539 + $19.50× M

Which gives

$65,054 - $12,539 =  $19.50× M - $8.25 × M

$52515 = $11.25 × M

M = $52515/$11.25 = 4668 books.