Question

Anna is considering writing and publishing her own book. She estimates her revenue equation as R=6.37x, and her cost equation as C=10,071+1.08x, where x is the number of books she sells. Find the minimum number of books she must sell to make a profit.

Answer 1

Anna must sell at least 1,904 books to make a profit as this is the point where her revenue from selling books will exceed her total costs.

Step-by-step explanation:

In order to determine the minimum number of books Anna must sell to make a profit, we need to find the point where her total revenues exceed her total costs.

The revenue equation given is R = 6.37x, and the cost equation is C = 10,071 + 1.08x, where x represents the number of books sold.

Profit occurs when R > C, so:

1. Set up the inequality 6.37x > 10,071 + 1.08x.
2. Subtract 1.08x from both sides to get 5.29x > 10,071.
3. Divide both sides by 5.29 to isolate x, yielding x > 1903.02.

Since Anna can't sell a fraction of a book, she must sell at least 1,904 books to start making a profit.

Answer 2

The minimum number of books she must sell to make a profit is 1904.

Step-by-step explanation:

Anna is considering writing and publishing her own book. She estimates her revenue equation as R = 6.37x, and her cost equation as C = 10,071 + 1.08x, where x is the number of books she sells.

So, the condition for no loss-no gain is, C = R

⇒ 10071 + 1.08x = 6.37x

⇒ 5.29x = 10071

⇒ x = 1903.78

Therefore, the minimum number of books she must sell to make a profit is 1904. (Answer)