A business is said to break even when their costs are equal to their revenues (income).
To bring a new book to market, a publisher has fixed costs (such as layout and editing) of $21,400, and per-book costs (such as printing and royalties) of $4.20. Write an equation relating y, the publisher's costs, to x, the number of books they print.
y = 21400 +4.20x
When the book is sold, the publisher receives $6.05 per book. Write an equation relating y, the publisher's revenue, to x, the number of books they sell.
y = 6.05x
Assuming the publisher sells every book that they print, you can find the break-even point by combining your equations above into a system. By hand or using your calculator, solve the system, and use your solutions to answer the questions below.
How many books must the publisher sell to break even? Round your answer up to the next whole book.
books
What will the publisher's revenue be if they sell this many books? Use your rounded value, above, to answer this question.
$
The break-even point can be found by setting the publisher's costs equal to their revenue:
21400 + 4.20x = 6.05x
Subtract 4.20x from both sides:
21400 = 1.85x
Divide by 1.85 to solve for x:
x = 11567.57
Rounded up to the next whole book, the publisher must sell 11568 books to break even.
Plugging this value back into the revenue equation:
y = 6.05 * 11568
y = $69883.40
If the publisher sells 11568 books, their revenue will be $69,883.40.