z varies directly as x^2 and inversely as y^2 . If z = 165
when x = 4 and y = 7 , find z if x = 9 and y = 6 . (Round
off your answer to the nearest hundredth.)
For all proportion problems, start with this:
Varying "directly" or product of "jointlys" or 1 if none
quantity = k · ----------------------------------------------------------
inversely variable or product of "inverselys" or 1 if none
In this problem the varying quantity is z.
We have one "directly", x². We have one inversely, y². So we have x²
on top and y² on the bottom:
z = k·
one set of values isz = 165 when x = 4 and y = 7
Substitute these values:
165 = k·
165 = k·
Multiply both sides by 
= k
Now substitute for k in the first equation:
z = k·
z = ·
>>...find z if x = 9 and y = 6 ...<<
Substitute those values
z = ·
z = ·
z = 1136.953125
Round to
z = 1136.95
Edwin
