It costs a publishing company \( \$ 49,326 \) dollars to make books. The \( \$ 49,326 \) is a fixed cost or a cost that cannot change. To help the publishing company sell the books, a marketing company charges \( \$ 4.1 \) dollars for each book sold. If the company charges \( \$ 10 \) dollars per book, how many books should they sell to break even? (Round your final answer to the nearest whole number). ?

To determine how many books the publishing company should sell to break even, we need to consider the fixed cost and the variable cost associated with selling the books. Given: - Fixed cost: $49,326 - Variable cost per book: $4.1 - Selling price per book: $10 Let's denote the number of books to be sold as \( x \). The total cost of selling \( x \) books can be calculated as: \[ \text{Total cost} = \text{Fixed cost} + \text{Variable cost} \times x \] Substitute the given values: \[ \text{Total cost} = 49,326 + 4.1x \] The total revenue from selling \( x \) books at $10 per book is: \[ \text{Total revenue} = 10x \] To break even, the total revenue should equal the total cost: \[ 10x = 49,326 + 4.1x \] Now, we can solve for \( x \) to find the number of books the company should sell to break even. Solve the equation by following steps: - step0: Solve for \(x\): \(10x=49326+4.1x\) - step1: Move the variable to the left side: \(10x-4.1x=49326\) - step2: Subtract the terms: \(5.9x=49326\) - step3: Divide both sides: \(\frac{5.9x}{5.9}=\frac{49326}{5.9}\) - step4: Divide the numbers: \(x=\frac{493260}{59}\) The number of books the publishing company should sell to break even is \( \frac{493260}{59} \) books. To round this to the nearest whole number, we calculate \( \frac{493260}{59} \) and round the result to the nearest whole number. Round the number by following steps: - step0: Round the number to the nearest whole number: \(493260/59\) - step1: Rewrite in decimal: \(8360.338983\) - step2: Round the number to the nearest whole number: \(8360\) The publishing company should sell approximately 8,360 books to break even.