# Question 0cfad

Jul 29, 2015

$n = 17$

#### Explanation:

So, you know that the price of a single copy varies depending on the number of books that are being purchased.

More specifically, if you buy less than 20 books, you pay $\text{16 Rs}$ per book, but that if you buy 20 or more books, you only have to pay $\text{13 Rs}$ per book.

First, figure out how much money you have to pay when you buy 20 books.

20color(red)(cancel(color(black)("books"))) * "13 Rs"/(1color(red)(cancel(color(black)("book")))) = "260 Rs"#

Now, you need to figure out the minimum number of books you that can buy at full price for more money.

If $n$ rpresents the number of books, which you know must satisfy the condition $n < 20$, then you have

$n \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{books"))) * ("16"color(purple)(cancel(color(black)("Rs"))))/(1color(red)(cancel(color(black)("book")))) > 260color(purple)(cancel(color(black)("Rs}}}}$

$n \cdot 16 > 260$

Divide both sides of the equation by $16$ to get

$\frac{n \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{16}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{16}}}} > \frac{260}{16}$

$n > \frac{65}{4}$

$n > 16.25$

The minimum number of books that you can buy at full price and still pay more than you would for a 20-book purchase at a discount is

$n = \textcolor{g r e e n}{17}$