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 $23,066, and the variable costs will be $22.25 per book. With the other method, the one-time fixed costs will total $66,195, and the variable costs will be $11.50 per book. For how many books produced will the costs from the two methods be the same?

Answer 1

The small publishing company has to publish 4012 new books so they can have the same cost from the two methods.

Explanation:

Let's take the equation.

22.25X + 23066 = 11.50X + 66195

We have the unit cost for book in the two sides + the two fixed cost, and we want to be the same, that's why we put the =.

So let's solve it.

22.25X - 11.5X = 66195 - 23066

10.75X = 43129

x=43129 / 10.75

x =4012

Let's check

22.25 x 4012 + 23066 = 112333

11.50 x 4012 + 66195 = 112333.

:)