As both #x# and #z# are related to #y# we can express them as follows:

Given:#" "color(red)( y)" "color(blue)(alpha)" "color(red)( x)" "color(blue)(alpha)" "color(red)( 1/z^2)#

Where #alpha# means proportional to.

Let #k" and "c# be constants of variation. Then we have:

#y=k x=c/z^2#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Determine the values of "k" and "c)#

Base condition is that at #y=20 ; x=50 ; z=5#

#color(brown)("To determine "k)#

#=>y=kx" "->" "20=k(50)#

Divide both sides by 50

#20/50=kxx50/50" "#

but #50/50=1#

#color(brown)(k=20/50=2/5#

'...........................................................

#color(brown)("To determine "c)#

#=>y=c/z^2" "->" "20=c/(5^2)#

Multiply both sides by 25

#color(brown)(c=20xx25= 500)#

'.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Determine the value of "y" at "x=3)#

#y=kx " "->" " y=2/5xx3#

#color(blue)( y=6/5)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Determine the value of "y" at "z=6)#

#y=c/z^2" "->" "y=500/6^2#

#y=13 8/9 -> 125/9#