Variation Equations. I have tried :(

Question

The variable Z is directly proportional to X, and inversely proportional to Y. When X is 5 and Y is 19, Z has the value 2.8947368421053.

What is the value of Z when X = 12, and Y = 24

Answer 1

The variable Z is directly proportional to X

 

      z α x

 

and inversely proportional to Y:

 

      z α 1/y

 

So the equation of variation is z = k(x/y) where k is the constant of proportionality.  To find k, plug in the point you are given z = 2.8947368421053 when x = 5 and y = 19:

      z = k(x/y)

      2.8947368421053 = k(5/19)

      (2.8947368421053)*19/5 = k

      11 = k

 

So the equation is:

 

      z = 11*(x/y)

 

For x = 12 and y = 24:

 

      z = 11*(12/24) = 5.5