How Long is Duke the Dog?

Date: 09/04/2001 at 18:19:22
From: Ivy
Subject: Algebra/Problem of the Week

Bobby has a dog named Duke. Duke's head is 6 inches long, his tail is 
as long as his head plus half the length of his body, and his body is 
as long as his head and tail combined. How long is Duke the dog?  

Please tell me how to figure this out.

Date: 09/05/2001 at 11:31:21
From: Doctor Ian
Subject: Re: Algebra/Problem of the Week

Hi Ivy,

Let's use a picture to help us keep track of what we know, and what 
we're trying to find out:

                                   H = 6
                                   +----+
   T = H + B/2                     |    |
   ------------- +---------------+ +-----
                 |               |
                 |               |
                 +---------------+
                   B = H + T

I'm using H to stand for the length of the head (which we know to be 
6 inches), B to stand for the length of the body (which we know to be 
the combined length of the head and the tail), and T to stand for the 
length of the tail (which we know to be the length of the head plus 
half the length of the body). 

Now, note that since T = H + B/2, we can do this:

                                   H = 6
                                   +----+
   T = H + B/2                     |    |
   ------------- +---------------+ +-----
                 |               |
                 |               |
                 +---------------+
                   B = H + T

                     = H + (H + B/2)

                     = 2H + B/2

                     = 2*6 + B/2

If you solve that equation for B, you'll know the length of the body; 
and with the length of the head, that will tell you the length of the 
tail.  Add them up, and you'll have the length of the dog. 

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/