Question

If x and y vary inversely.then using the following table and find the value of x for y 10.
x. - 5
y. - 30

Answer 1

x=-5

y=-30

xy=150

10x=150

x=15

Answer 2

The value of x = 15

Given :

x and y vary inversely and x = - 5 when y = - 30

To find :

The value of x for y = 10.

Solution :

Step 1 of 3 :

Form the equation

Here it is given that x and y vary inversely

$\displaystyle \sf{x \propto \: \frac{1}{y} }$

$\displaystyle \sf{ \implies \: x = \: \frac{k}{y} }$

$\displaystyle \sf{ \implies \: xy = k \: \: \: - - - - (1) }$

Where k is a non zero real number

Step 2 of 3 :

Find the value of k

x = - 5 when y = - 30

From Equation 1 we get

$\displaystyle \sf{ \: - 5 \times (-30) = k}$

$\displaystyle \sf{ \implies \: k = 150}$

Equation 1 gives

$\displaystyle \sf{xy = 150}$

Step 3 of 3 :

Find the value of x

Now for y = 10 we have

$\displaystyle \sf{ \implies \:x \times 10 = 150}$

$\displaystyle \sf{ \implies \: 10x =150}$

$\displaystyle \sf{ \implies \:x = 15}$

Hence the required value of x = 15