If y varies jointly with X and z and y=9 when x=2 and z=9 find x when y = 105 and z = 3

x = 70

Step-by-step explanation:

The variation model we'll need here is y = kxz, where k is the constant of proportionality. We are told that when y = 105, x = 2 and z = 9. This gives us enough info with which to calculate k:

9 = k (2) (9), or 1 = 2k, or k = 1/2.

Then the governing equation is

y = (1/2) xz.

If y = 105 when z = 3, then we have 105 = (1/2) (x) (3).

To solve this for x, first multiply both sides by 2, obtaining 210 = 3x.

Finally, we divide both sides by 3, obtaining the final result x = 70