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 (suchas printing). The one-time fixed costs will total $30456. The variable costs will be $10 per book. The publisher will sell the finished product to bookstores at aprice of $21.75 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Answer 1

Let x be the number of books that need to be sold, then for the cost of the production and the profit to be the same we can set the following equation:

`30456+10x=21.75x\text{.}`

Subtracting 10x from both sides of the equation we get:

`30456=21.75x-10x,`

adding like terms we get:

`30456=11.75x\text{.}`

Dividing by 11.75 we get:

`x=2592.`

Then the producer must sell 2592 books.

Answer: 2592.