Question

If x and y varies inversely as each other and x = 8 when y = 32 . FIND Y WHEN X = 16

Answer 1

Step-by-step explanation:

x = 8; 32

y = 16; y2

since it is inverse proportion

therefore, 8×32 ÷ 16 = 16

Answer 2

The value of y = 16

Given :

• x and y varies inversely as each other

• x = 8 when y = 32

To find :

The value of y when x = 16

Solution :

Step 1 of 3 :

Form the equation

Here it is given that x and y varies inversely as each other

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

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

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

Where k is a non zero real number

Step 2 of 3 :

Find the value of k

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

x = 8 when y = 32 gives

$\displaystyle \sf{ \implies \: (8 \times 32) = k }$

$\displaystyle \sf{ \implies \: k = 256 }$

Equation 1 gives

$\displaystyle \sf{ \implies \: xy = 256}$

Step 3 of 3 :

Find value of y when x = 16

$\displaystyle \sf{ \implies \: xy = 256}$

For x = 16 we have

$\displaystyle \sf{ \implies \: 16y = 256}$

$\displaystyle \sf{ \implies \: y = 16}$

Hence the required value of y = 16