Golf Balls

Date: 04/13/97 at 17:55:05
From: Anonymous
Subject: Golf Balls

I need help pretty quickly on a problem.  It goes like this:
Angie bought some golf balls for $14.  If each ball had cost $0.25 
less she could have bought one more ball for the same amount of money.  
How many golf balls did Angie buy?

Any help you can give as to the answer, and more importantly, how to 
solve it, would be appreciated.  

Thanks.  Mike Blea

Date: 04/14/97 at 10:35:53
From: Doctor Anthony
Subject: Re: Golf Balls

Let x = number of golf balls Angie bought.
    c = cost of each ball.

Then   

   cx = 14  so  c = 14/x.

We also have  

            (c-.25)(x+1) = 14
       (14/x - .25)(x+1) = 14
  14 + 14/x - .25x - .25 = 14
       14/x - .25x - .25 = 0
      14 - .25x^2 - .25x = 0
      .25x^2 + .25x - 14 = 0
            x^2 + x - 56 = 0

   (x-7)(x+8) = 0   and so x = 7    c = 14/x = 2.

So Angie bought 7 golf balls at $2 each.

It is also true that 8 x 1.75 = 14  so she could have bought 8 golf 
balls if the cost had been $1.75  

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/