Answered

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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?

Sagot :

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:

[tex]30456+10x=21.75x\text{.}[/tex]

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

[tex]30456=21.75x-10x,[/tex]

adding like terms we get:

[tex]30456=11.75x\text{.}[/tex]

Dividing by 11.75 we get:

[tex]x=2592.[/tex]

Then the producer must sell 2592 books.

Answer: 2592.

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