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/ |
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