Question

If x and y varies inversely as each other when x = 16 , y = 4 . Find y when x = 8 ​

Answer 1

The statement is expressed as y∝1x

inverse means 1variable

To convert to an equation introduce k, the constant of variation.

y=k×1x

⇒y=kx

To find k use the given condition that y = 8 when x = 4

8=k4⇒k=4×8=32

⇒ equation is ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯∣∣∣22y=32x22∣∣∣−−−−−−−−−−−−

x=16→y=3216

⇒y=2 when x=16