Question 1070114: 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). The one-time fixed costs will total $50,560. The variable costs will be $8.50 per book. The publisher will sell the finished product to bookstores at a price of $24.50 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?
Found 2 solutions by Zucchini, Theo:
Answer by Zucchini(70)   (Show Source):
You can put this solution on YOUR website! First, write the equation for the production of the books:
p = 8.50b + 50,560
This equation shows that for the production, $8.50 is paid per book and $50,560 have to paid anyway.
Now, write the equation for the sales:
s = 24.50b
Now, set both of the equations equal to each other because the sales and production money have to be equal, as asked in the question.
p = s
8.50b + 50,560 = 24.50b
50,560 = 16b
3,160 = b
3,160 books must be produced and sold.
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! x = number of books.
cost = 50,560 + 8.50 * x
revenue = 24.5 * x
break even is when revenue equals cost.
revenue equals cost equation becomes:
24.5 * x = 50,560 + 8.50 * x
subtract 8.50 * x from both sides of the equation to get:
24.5 * x - 8.5 * x = 50,560
combine like terms to get:
16 * x = = 50,560
divide both sides of the equation by 16 to get:
x = 50,560 / 16 = 3160.
replace x in the original cost and revenue equations to get:
cost = 50,560 + 8.50 * x becomes cost = 50,560 + 8.50 * 3160 which gets you cost = 77,420.
revenue = 24.5 * x becomes revenue = 24.5 * 3160 which gets you revenue = 77,420.
solution looks good.
he will have to sell 3160 books to break even.
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