Question

x is inversely proportional to y. When x = 3, y = 2. Find the value of y when x = 18.

Answer 1

Answer:

The value of y is $\frac{1}{3}$

Step-by-step explanation:

We have the following relation given to us that the value of x is inversely proportional to that of y, which means that any increase in the value of x will decrease the value of y.

Therefore we have been given,

x ∝ $\frac{1}{y}$

The above-given are in inverse proportion,

hence we have $x_{1} y_{1} = x_{2} y_{2}$

In the question above, we have been given that,

$x_{1} = 3$ and $y_{1} = 2$

$x_{2} = 18$ and we have to calculate $y_{2}$

Therefore putting all the given values in the above equation we have,

$x_{1} y_{1} = x_{2} y_{2}$

⇒$(3) (2) = (18)y_{2}$

⇒ 6 = 18$y_{2}$

⇒$y_{2}$ = 6 ÷ 18

⇒$y_{2}$ = $\frac{1}{3}$

Therefore the value of y whenever the x= 18 is $\frac{1}{3}$

Answer 2

Given: x = 3, y = 2

To find The value of y when x = 18.

Solution: The concept of proportional which is inverse is a phenomenon where if a system increases then the opposite thing that is decreases will happen on that particular system.

Given  x∝(1/y)  [∵x is inversely proportional to y]

⇒x=(k/y)   [ To make the above form in the equation we have taken a

                                                                          constant k]]

⇒(x×y)=k  

⇒k=(x×y)    [rearranging the sides]

⇒k=(3×2)   [given x=3, y=2]

⇒k=6   [finding the value of k so that it can be implemented on the next case and the value of k will remain the same as it is a constant]

Now to determine the value of y when x=18, we have

x=(k/y)

⇒(x×y)=k

⇒y=k/x

⇒y=6/18   [substituting the values of k and x]

⇒y=1/3

Hence the value of y when x = 18 is 1/3.