A small publishing company is planning to publish a new book. The production costs will include one-time fixed costs (editing) and variable costs (printing). One time fixed cost will total $76,322. The variable costs will be $10 per book. The publisher will sell the finished product to the book store at a price of $25.50 per book. How many books must the publisher produce and sell that the production costs will equal the money from sales?

the answer is 4924 books..how would i go about solving this problem im suck. Thanks for the help in advance!

Let B = the "break even" number of books.

Production costs=$76,322 + B * $10
Total Sales = B * $25.50
Setting these equal...
Total sales = Production costs
or...
$76,322 + B * $10 = B * $25.50
Solve for B

To solve this problem, you need to find the number of books that must be produced and sold in order for the production costs to equal the amount of money from sales.

Let's break down the calculation step by step:

Step 1: Calculate the total variable costs (printing) per book.
Variable costs per book = $10

Step 2: Calculate the total one-time fixed costs (editing).
One-time fixed costs = $76,322

Step 3: Calculate the total cost per book.
Total cost per book = Variable costs per book + One-time fixed costs
Total cost per book = $10 + $76,322 = $76,332

Step 4: Calculate the selling price per book.
Selling price per book = $25.50

Step 5: Determine the profit per book.
Profit per book = Selling price per book - Total cost per book
Profit per book = $25.50 - $76,332 = -$75,306.50

Since the profit per book is negative, it means that the publisher is losing money on each book sold. Therefore, they need to sell enough books to cover the production costs.

Step 6: Set up an equation to find the break-even point (when revenue equals production costs).
Number of books * Selling price per book = Total production costs

Let's use the variable 'x' to represent the number of books.

x * $25.50 = $76,322 + $10x

Step 7: Solve the equation for 'x'.
25.50x = 76,322 + 10x
15.50x = 76,322
x = 76,322 ÷ 15.50
x ≈ 4924 (rounded to the nearest whole number)

Therefore, the publisher must produce and sell approximately 4924 books in order to equalize the production costs with the money from sales.