SOLUTION: The variable Z is directly proportional to X, and inversely proportional to Y. When X is 3 and Y is 6, Z has the value 9.5. What is the value of Z when X = 8, and Y = 12

Algebra ->  Sequences-and-series -> SOLUTION: The variable Z is directly proportional to X, and inversely proportional to Y. When X is 3 and Y is 6, Z has the value 9.5. What is the value of Z when X = 8, and Y = 12      Log On


   

Question 981073: The variable Z is directly proportional to X, and inversely proportional to Y. When X is 3 and Y is 6, Z has the value 9.5.
What is the value of Z when X = 8, and Y = 12
Found 2 solutions by ikleyn, stanbon:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!

The fact that  "the variable  Z  is directly proportional to  X,  and inversely proportional to  Y"  (which is the given condition)  means that

Z = k%2A%28X%2FY%29,

where  k = const  (is a constant value).  If you substitute  X=3,  Y=6  and  Z=9.5  into this formula,  you will get

9.5 = k%2A%283%2F6%29 = k%2F2.

Hence,  k = 9.5%2A2 = 19.

Thus our formula for  Z  is

Z = 19%2A%28X%2FY%29.

Now,  if you substitute  X=8  and  Y=12  into the last formula,  you will get

Z = 19%2A%288%2F12%29 = %2819%2A8%29%2F12 = 12.667 (approximately).

It is the answer to your question.


Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The variable Z is directly proportional to X,
and inversely proportional to Y.
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Z = K*X/Y
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When X is 3 and Y is 6, Z has the value 9.5.
Solve for "K"::
9.5 = K*3/6
K = 19
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What is the value of Z when X = 8, and Y = 12
Equation:
Z = 19*X/Y
Z = 19*8/12
Z = (2/3)19 = 38/3 = 12 2/3
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Cheers,
Stan H.
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