Date: 9/15/96 at 14:10:46 From: Anonymous Subject: K-triple Let a "k-triple" be defined as (k/2, k, 3/2k) for any number k. Which of the following is a k-triple? a. (0, 5, 10) b. (4 1/2, 5, 6 1/2) c. (25, 50, 75) d. (250, 500, 1000) e. (450, 500, 650) I do not understand this question. Could you please explain it?
Date: 9/16/96 at 11:45:18 From: Doctor Mike Subject: Re: K-triple Hello, This looks like an exercise to help you get used to abstract symbolic thought processes, which is a step or 2 beyond just numerical calculations. The idea of a "k-triple" is a made-up one having no importance, except that it helps to get you to think about some important things. First of all, the idea of a triple here is just a grouping of three things in a particular order. The fact that a variable "k" is used just means that not just one triple is involved, but perhaps many of them, all of which follow a particular pattern. What pattern? For one thing, the first one in the k-triple must be exactly half of the second one. With this observation alone you can eliminate (a.) and (b.) and (e.). Choices (c.) and (d.) both work SO FAR since 25 is half of 50 and 250 is half of 500, respectively. The pattern also requires that the last in the k-triple must be 3/2 times the middle one. Is 3/2*(500) equal to 1000? No, so (d.) does not follow the pattern. Is 3/2*(50) equal to 75? Yes, so (c.) is the only one of the five that fully qualifies. Clear? (1,2,3) and (2222,4444,6666) and many more are also k-triples. I hope this helps. -Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/
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