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 $13,705, and the variable costs will be $19.50 per book. With the other method, the one-time fixed costs will total $60,661, and the variable costs will be $9.75 per book. For how many books produced will the costs from the two methods be the same?

Answer 1

4816 books

Explanation:

Set up the equations for both production methods

y = 19.5x + 1305

y= 9.75x + 60661

Solve for x (number of books at the intercept of both equations)

9.75x + 60661 = 19.5x + 13705

9.75x + 46956 = 19.5x (subtracted 13705 from both sides)

46956 = 9.75x (subtracted 9.75x from both sides)

x = 4816 (divided both sides by 9.75 to isolate x)

If you need the cost at which the two methods are the same, you can simply substitute x (which we now know is 4816) into any of the equations we made for the production methods