Question

A puzzle expert wrote a new sudoku puzzle book. His initial costs arethree hundred and twenty-five dollars. Binding and packaging each bookcosts sixty cents. The price of the book is one dollar and ninety cents.How many books must be sold to break even? Enter an integer.

Answer 1

From the statement of the problem, we know that the costs are:

• $325, for the initial costs,

,

• $0.60, for binding and packaging ,each book,,

The price of each book is $1.90.

If n is the number of books sold, the total cost for product n books is:

• $325 for the initial costs,

,

• $0.60 * n for binding and packaging the n books.

,

•

The total cost is the sum of these quantities:

$\text{Cost = \ 325 + \ 0.60 }\cdot n.$

If the puzzle expert earns $1.90 for each book, for n books he will earn:

$\text{Earnings = \ 1.90 }\cdot n.$

The expert will break even when the total cost is equal to the earnings:

$\begin{gathered} \text{Cost = Earnings,} \\ 325+0.60\cdot n=1.90\cdot n\text{.} \end{gathered}$

Solving for n the last equation, we get:

$\begin{gathered} 325=1.90\cdot n-0.60\cdot n, \\ 325=1.30\cdot n, \\ n=\frac{325}{1.30}=250. \end{gathered}$

Answer

To break even, 250 books must be sold.