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). The one-time fixed costs will total $32,634 . The variable costs will be $8.75 per book. The publisher will sell the finished product to bookstores at a price of $24.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Information:

Fixed Cost = $32,634
Variable Cost = $8.75 per book.
Selling Price = $24.50 per book.

Define x:

Let x be the number of books sold.

Construct Equation:

For production cost to be equal auto money from sales:
⇒ 24.5x = 32634 + 8.75x 

Solve x:

24.5x = 32634 + 8.75x 

Take away 8.75x from both sides:
15.75x = 32634

Divide both sides by 15.75:
x = 2072

Answer: The publisher must sell 2072 books.