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 $50,898 , and the variable costs will be $9 per book. With the other method, the one-time fixed costs will total $12,632 , and the variable costs will be $22.25 per book. For how many books produced will the costs from the two methods be the same?

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23-12-2016
Mathematics

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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 $50,898 , and the variable costs will be $9 per book. With the other method, the one-time fixed costs will total $12,632 , and the variable costs will be $22.25 per book. For how many books produced will the costs from the two methods be the same?

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You can express the price of printing n books using either method algebraically. Using the first method, to produce n books costs $50 898 + $9n. Using the second method, to produce n books costs $12 632 + $22.25n. If the costs to produce x books costs the same for both methods, we can say $50 898 + $9x = $12 632 + $22.25x. Isolating x, we have $38 266 = $13.25x. Dividing both sides of the equation by $13.25 gives you x = 2 888, where x is the number of books at which the production costs through each method are the same.