Y varies directly as x and inversely as z. y=2/9 when x=2 and z=6. Find y when x=3 and z=5.

I can solve this on my own if i know the setup. is directly and inversely meaning that the setup is y=x/z?

Question

Y varies directly as x and inversely as z. y=2/9 when x=2 and z=6.  Find y when x=3 and z=5.  

I can solve this on my own if i know the setup. is directly and inversely meaning that the setup is y=x/z?

phi · Answer

y varies directly as x means
y= kx  for some number k
y varies inversely as z means y= m/z  for some number m

rainbow_dash · Answer

Oh, is K the constant?  finding that will allow me to find the new equation, right

phi · Answer

putting them together it looks like 
y= kx/z

use the given values to find k.  now you can find y for other values of x,z

rainbow_dash · Answer

Okay so it'll be y=kx/z, which is 2/9=K2/6.  
then 2/9*6=K2, divide by 2 equals K.  then I'd take K and plug in to y=K3/5..

phi · Answer

yes.  though I would be tempted to reduce 2/6 to 1/3 because it looks simpler. But either way...

rainbow_dash · Answer

okay the answer is y = 2/5 in the final result i'm thinking. thanks! it's just the equations/formulas with variation (or any math for that matter) always escape me during the summer.

phi · Answer

looks good.