Question #0cfad

1 Answer
Jul 29, 2015

Answer:

#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 #"16 Rs"# per book, but that if you buy 20 or more books, you only have to pay #"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

#ncolor(red)(cancel(color(black)("books"))) * ("16"color(purple)(cancel(color(black)("Rs"))))/(1color(red)(cancel(color(black)("book")))) > 260color(purple)(cancel(color(black)("Rs")))#

#n * 16 > 260#

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

#( n * color(red)(cancel(color(black)(16))))/color(red)(cancel(color(black)(16))) > 260/16#

#n > 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 = color(green)(17)#