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
$14,532
, and the variable costs will be
$19.25
per book. With the other method, the one-time fixed costs will total
$34,447
, and the variable costs will be
$10.50
per book. For how many books produced will the costs from the two methods be the same?

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 
$14,532
, and the variable costs will be 
$19.25
 per book. With the other method, the one-time fixed costs will total 
$34,447
, and the variable costs will be 
$10.50
 per book. For how many books produced will the costs from the two methods be the same?

seascorpion1 · Answer

you should graph these as a y=ax+b (slope-intercept form): 

$$y_1=14532+19.25b$$

$$y_2=34447+10.5b$$ where b is the number of books.

Then set $$y_1=y_2$$ and solve for b.