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 $47,642 , and the variable costs will be $9.25 per book. With the other method, the one-time fixed costs will total $23,792 , and the variable costs will be $20.50 per book. For how many books produced will the costs from the two methods be the same?

Respuesta :

Answer:

2120 books


Step-by-step explanation:

Let the number of books be [tex]x[/tex]

  • For the first method, we can write the cost equation as:

Cost = [tex]47,642+9.25x[/tex]

  • For the second method, we can write the cost equation as:

Cost = [tex]23,792+20.50x[/tex]


Since we want cost to be same, we equate the 2 equations of cost and solve for x, the number of books, to get our answer:

[tex]47,642+9.25x=23,792+20.50x\\47,642-23,792=20.50x-9.25x\\23,850=11.25x\\x=\frac{23,850}{11.25}\\x=2120[/tex]


The cost for both methods will be same for 2120 books

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