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 $22,916, and the variable costs will be $23
per book. With the other method, the one-time fixed costs will total $62,454, 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?
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Fixed costs don't change, so they're just numbers. We put those straight into the equation.
Variable costs are represented by.. variables! Letters like x and y.
Start by writing out a math statement that represents the first method.
Fixed costs = 22916
Variable costs = # of books x 23
If we put "# of books" in the equation, it'll be hard to read, so we call it something easier like "b".
Our statement for the first method is:
22916 + (23 x b)
or 22916 + 23b
$22,916 that always gets paid + 23 per book (for however many books)
Now we do the same for the second method.
Fixed costs: 62454
Variable costs: 9.75 x # of books (or 9.75 x b)
Our statement for the second method is:
62454 + (9.75 x b)
or 62454 + 9.75b
Are we done? We have to check what the problem is actually asking:
"For how many books produced will the costs from the two methods be the same?"
We don't know that yet. How do we get it?
We want to know when the two methods are the same or... equal to each other. So, we set them equal to each other!
22916 + 23b = 62454 + 9.75b
Now, solve for b and you have your answer.