ONE MORE AND I SHOULD BE DONE

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
$68,694
, and the variable costs will be
$10.25
per book. With the other method, the one-time fixed costs will total
$22,305
, and the variable costs will be
$22
per book. For how many books produced will the costs from the two methods be the same

Answer 1

Let x be the number of books produced.

 

With method A, the total costs would be the fixed cost of 68694 plus 10.25 per book, or 10.25x.  In other words 68694 + 10.25x

 

By the same reasoning, the total costs With method B would be 22305 + 22x.

 

So set these two expressions equal to each other.  Whatever x comes out to be in that equation will be the number of books resulting in equal costs between the two methods.

 

So 68694 + 10.25x = 22305 + 22x

 

Subtract 22305 from both sides:

46389 + 10.25x = 22x

Subtract 10.25x from both sides:

46389 = 11.75x

 

Divide both sides by 11.75:

3948 = x

 

So the answer is 3948 books.

 

Plug this back for x in either cost equation to get the total cost:

22305 + 22 * 3948 = 109161

 

To check the result, plug the value for x into the other equation to make sure it is the same:

68694 + 10.25 * 3948 = 109161