Question

If $x$ varies inversely with $y$ and $x = 4$ when $y = 9$, how do you find $x$ when$y = 6$?

Answer 1

Hint: Here we must know that when $x$ varies inversely with $y$ we can write it in the form $x\alpha \dfrac{1}{y}$ and now we can remove the inversely proportional sign with any constant say $k$ and write it as $x = \dfrac{k}{y}$ and then find the value of constant by the information given. Then we can find the required value of any variable needed.

Complete step by step solution:
Here we are given that $x$ varies inversely with $y$
So we can say that $x{\text{ and }}y$ are inversely proportional to each other.
Hence we can write it in the form which may be represented as $x\alpha \dfrac{1}{y}$ and now we can remove the inversely proportional sign with any constant say $k$ and write it as
$x = \dfrac{k}{y}$$ - - - - (1)$
 We are also given that $x = 4$ when$y = 9$
So we can put the above given value in the equation (1) and get the required value of the constant
So substituting $x = 4$ and $y = 9$ in equation (1) we get:
$x = \dfrac{k}{y}$
$4 = \dfrac{k}{9}$
Solving it we will get that $k = \left( 4 \right)\left( 9 \right) = 36$
Now we get the equation as $xy = 36$$ - - - - (2)$
Now we are given to find the value of the variable $x$ when the $y = 6$
So we just need to put this value $y = 6$ in the equation (2) and we will get:
$xy = 36$
$x\left( 6 \right) = 36$
So solving this we can easily get the value of the required variable as:
$x = \dfrac{{36}}{6} = 6$

Hence we can say that when $y = 6,x = 6$

Note:
Here the student can also be told that the variation in the two variable is not inverse and it is linear then we need to take the directly proportional sign and with the constant, we will get the equation as:
$x = ky$