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 $67,666, and the variable costs will be $10.50 per book. With the other method, the one-time fixed costs will total $18,775, and the variable costs will be $21.25 per book. For how many books produced will the costs from the two methods be the same?

Answer 1

For 4548 books produced, the costs from two methods will be same.

Step-by-step explanation:

Given,

Fixed cost for method one = $67,666

Variable costs = $10.50 per book

Let,

x be the number of books.

O(x) = 10.50x+67666

Fixed cost for method two = $18,775

Variable costs = $21.25 per book

T(x) = 21.25x+18775

For the costs to be same;

T(x) = O(x)

$21.25x+18775=10.50x+67666\\21.25x-10.50x=67666-18775\\10.75x=48891$

Dividing both sides by 10.75

$\frac{10.75x}{10.75}=\frac{48891}{10.75}\\x=4548$

For 4548 books produced, the costs from two methods will be same.

Keywords: function, division

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