https://file.aiquickdraw.com/mathbot/file/1728347563135odmc7gls.jpg

This problem asks for the break-even point, where total costs equal total revenue. Let's break it down:

### Given:
- Fixed costs = $71,946
- Variable cost per book = $9.25
- Selling price per book = $25

### Let $ x $ represent the number of books that need to be sold.

1. **Total Costs**:
   Total costs include both fixed and variable costs. The total cost is given by:
   \[
   \text{Total Cost} = \text{Fixed Cost} + (\text{Variable Cost per book} \times x)
   \]
   Substituting values:
   \[
   \text{Total Cost} = 71,946 + 9.25x
   \]

2. **Total Revenue**:
   The total revenue is given by the selling price per book times the number of books sold:
   \[
   \text{Total Revenue} = 25x
   \]

3. **Break-even Point**:
   To find the break-even point, we set total revenue equal to total costs:
   \[
   25x = 71,946 + 9.25x
   \]

4. **Solve for $ x $**:
   First, subtract $ 9.25x $ from both sides:
   \[
   25x - 9.25x = 71,946
   \]
   Simplify:
   \[
   15.75x = 71,946
   \]
   Now, divide both sides by 15.75:
   \[
   x = \frac{71,946}{15.75} = 4,569.27
   \]

Since the number of books must be a whole number, the publisher needs to sell **4,570 books** to break even.

---

Would you like further explanation or clarification on any part? Here are 5 related questions to expand on this:

1. How does the fixed cost affect the break-even point?
2. What would happen if the variable cost per book increased?
3. How many books would need to be sold if the selling price changed to $30 per book?
4. Can the break-even point be reduced by lowering the fixed costs? How?
5. How does a change in both fixed and variable costs impact the break-even point?

### Tip:
To minimize the break-even point, consider either increasing the selling price or reducing production costs (fixed or variable).

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 $71,946. The variable costs will be $9.25 per book. The publisher will sell the finished product to bookstores at a price of $25 per book. How many books must the publisher produce and sell so that the production costs will equal the money from sales?

Find out how many books a small publishing company must sell to break even, given fixed costs of $71,946, a variable cost of $9.25 per book, and a selling price of $25. This problem uses algebra and linear equations to calculate the break-even point, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation