Question 118048: FIND THE CONSTANT OF VARIATION K.
m varies directly with n: m = 144 when n = 8.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! By saying that m varies directly with n, the problem is telling you that if n increases, then
m must increase also in proportion to the increase in n.
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This being the case we can write the equation:
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m = Kn
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Notice that if n doubles, then m will double also. If n triples, then m will triple also.
And so on. In other words, m is varying directly in proportion to the variation in n.
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The problem then tells you that m = 144 when n = 8. Substitute these two values into the
equation and you get:
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144 = K(8)
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Solve for K (the constant of variation) by dividing both sides of this equation by 8 and
you get:
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K = 144/8 = 18
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So the constant of variation is 18 and the equation becomes:
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m = 18n
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If n = 1 then m = 18. If n doubles to 2, then m = 18*2 = 36 so m has doubled also. If
n triples to 3, then m = 18*3 = 54, and that is 3 times the 18 that m was when n was only 1.
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Finally, when n = 8 then m = 18*8 = 144, just as the problem said it should be.
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Hope this helps you to understand the meaning of the constant of variation and how to find
it when you are told that direct variation is involved.
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