Question

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 $34,722. the variable costs will be $10.25 per book. the publisher will sell the finished product to bookstores at a price of $23.75 per book. how many books must the publisher produce and sell so that the production costs will equal the money from sales?

Explanation:

Step1: Define variables and equations

Let \( x \) be the number of books. The total production cost \( C \) is the sum of fixed costs and variable costs: \( C = 34722 + 10.25x \). The total sales revenue \( R \) is the price per book times the number of books: \( R = 23.75x \). We want to find \( x \) when \( C = R \).

Step2: Set up the equation

Set \( 34722 + 10.25x = 23.75x \).

Step3: Solve for \( x \)

Subtract \( 10.25x \) from both sides: \( 34722 = 23.75x - 10.25x \). Simplify the right side: \( 34722 = 13.5x \). Then divide both sides by \( 13.5 \): \( x=\frac{34722}{13.5} \). Calculate the division: \( x = 2572 \).

Answer:

\( 2572 \)