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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/
```
Associated Topics:
Elementary Word Problems
Middle School Algebra
Middle School Word Problems

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