z varies jointly as x and y, and inversely as w.

If z = 3 when x = 3, y = -2, and w = 4, find z when x = 6, y = 7, and w = -4.

Question

z varies jointly as x and y, and inversely as w.

If z = 3 when x = 3, y = -2, and w = 4, find z when x = 6, y = 7, and w = -4.

anonymous · Answer

21?

hartnn · Answer

z varies with x 
z = kx

z varies with y
z= ky

z varies inversely with w
z = k/w

combining all these

z = kxy/w

got this ?

anonymous · Answer

Is the answer 21?

hartnn · Answer

z = kxy/w and 
z = 3 when x = 3, y = -2, and w = 4
from these , can you try to get the value of k ?

anonymous · Answer

to my knowledge yes. but ask hartnn as well

hartnn · Answer

k comes out to be -2

hartnn · Answer

and yes, 21 its is :)

anonymous · Answer

^hartnn why is it to be the same k for all the three x,y,w

anonymous · Answer

Okay thanks!!!

hartnn · Answer

because there will only be one equation 
and so only one constant is needed.

you can take 3 different constants, but when combining , you will combine those 3 constants to one constant.

anonymous · Answer

^yes you are right hartnn. But it should not necessarily be the same k

hartnn · Answer

yes, correct.
 i just diddn't want to complicate things...

anonymous · Answer

True that it gives final single k, but having the same k for first 3 equations can mislead someone just trying to figure out the math out of it. Just saying

hartnn · Answer

true.
sorry.