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 p rinting). There are two production methods it could use. With one method, the one-time fixed costs will total $16,465, and the variable costs will be $20.50
per book. With the other method, the one-time fixed costs will total $37.815, and the variable costs will be $11.75 per book. For how many books produced will
the costs from the two methods be the same?

9514 1404 393

   2440

Step-by-step explanation:

The difference in fixed costs is ...

  37815 -16465 = 21350

The difference in variable costs is ...

  20.50 -11.75 = 8.75 . . . . per book

Then the number of books that must be produced for the difference in variable costs to be equal to the difference in fixed costs is ...

  21350/8.75 = 2440

For production of 2440 books, the costs of the two methods will be the same.

Additional comment

You can write expressions for total cost of each production method. When you set them equal and solve for the number of books, you find the math you end up doing is the same as that shown above.

since we know that the two functions are equal, f (x) = g

(x), therefore when we equate the two equations the result should be similar to

3x = x – 4:

a. f(x) = 3x, g(x) = x – 4

equating the two functions:

3x = x – 4             (correct)

so we now got our answer (a)