SOLUTION: FIND THE CONSTANT OF VARIATION K. m varies directly with n: m = 144 when n = 8.

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.
.
This being the case we can write the equation:
.
m = Kn
.
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.
.
The problem then tells you that m = 144 when n = 8. Substitute these two values into the
equation and you get:
.
144 = K(8)
.
Solve for K (the constant of variation) by dividing both sides of this equation by 8 and
you get:
.
K = 144/8 = 18
.
So the constant of variation is 18 and the equation becomes:
.
m = 18n
.
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.
.
Finally, when n = 8 then m = 18*8 = 144, just as the problem said it should be.
.
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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