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If y varies inversely with x and y = 6 when x = 3, then what is y when x = 2?

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2 Answers

When a variable y inversely varies with another x, it means that when y is doubled x is halved, when y is tripled x reduces to a third of original value.  This is shown below:
 
Suppose x is 4 when y is 2, then x is halved 2 when y doubled to 4.  When x is reduced to 1 (1/4th of the original value) then y is multiplied 4 times the original value to 2*4 = 8
 
In other words, x*y remains constant, which in the above example is 4*2.  
 
With the background above, we can answer the question
 
It is given in the question that y is 6 when x is 3.
 
Since y varies inversely with x, we know that x*y is constant which in this case is 6*3 = 18
 
When x changes to 2 y = 18/x =9  (since we know x*y = 18)
Since y varies inversely with x, we have:
y = a/x
y = 6 and x = 3
6 = a/3
6*3 = 3*a/3
18 = a
y = 18/x
 
When x = 2
y = 18/2 = 9