SOLUTION: Hi A man bought a number of books for $300.if each book cost 5 dollars more he could buy 10 books less for the same amount. Find the price of each book. Thanks

Let "p" be the price of one book.


Then the "conditional" price ("if-price") in other scenario would be (p+5) dollars.


The "if" equation then is


     -  = 10  books.


Multiply both sides by p*(p+5); then simplify


    300*(p+5) - 300p = 10p*(p+5)

    300p + 1500 - 300p = 10p^2 + 50p

    10p^2 + 50p - 1500 = 0

    p^2 + 5p - 150 = 0

    (p-10)*(p+15) = 0.


Only positive root p = 10 is the solution.


CHECK.   -  = 30 - 20 = 10 books.    ! Precisely correct !


ANSWER.  The price of one (of each) book is 10 dollars.