Answer:
[tex]x = \dfrac{36}{y}[/tex]
Step-by-step explanation:
We are given the following in the question:
x and y vary inversely.
[tex]x\propto \dfrac{1}{y}[/tex]
Removing the sign of proportionality and adding the constant of proportionality, we get,
[tex]x = k\times \dfrac{1}{y} = \dfrac{k}{y}[/tex]
where k is the constant of proportionality.
When x = 3, y = 12
Putting these value in the equation, we get,
[tex]3 = \dfrac{k}{12}\\\\\Rightarrow k = 12\times 3 = 36[/tex]
Putting value of k, we get,
[tex]x = \dfrac{36}{y}[/tex]
which is the required equation to model the given situation.
