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 $41,187, and the variable costs will be $8.75 per book. With the other method, the one-time fixed costs will total $15,491, and the variable costs will be $19.75 per book. For how many books produced will the costs from the two methods be the same?
Let x be the number of books produced.
For the first method, the total cost is $8.75x + $41,187.
For the second method, the total cost is $19.75x + $15,491.
Setting the two total costs equal to each other, we get $8.75x + $41,187 = $19.75x + $15,491.
Subtracting $8.75x and $15,491 from both sides, we get $41,187 - $15,491 = $19.75x - $8.75x.
Simplifying the left side gives $25,696 = $11x.
Dividing both sides by $11 gives x = $2,336.
Therefore, the costs from the two methods will be the same when 2336 books are produced. Answer: \boxed{2336}.