The tale of the dachshund is Half the length of its head. The head is 2/3 the size of its body. The total length of the dachshund is 60 cm. how long is each part of the dachshund?

Question

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Answer 1

Drawing a picture might help:

Since the tale is half the length of the head, we can say T = 1/2H or (multiplying both sides of the equation by 2) H = 2T

Since the head is 2/3 the body, we can say H = 2/3B or (multiplying both sides of the equation by 3/2) B = 3/2H. Combining this with H = 2T, we can say B = 3/2(2T) or B = 3T

Since the whole length is 60, we can say T + B + H = 60 or, substituting in what we developed above:

T + 3T + 2T = 60

6T = 60

T = 10

So the tail is 10 cm.

Using H = 2T, H = 2(10) or H = 20

So the head is 20 cm

Using B = 3T, B = 3(10) or B = 30

So the body is 30 cm.