If y varies jointly with x and z and y=40 when x=10 and z=9 find z when x =55 and y=105

  z = 189/44

Step-by-step explanation:

The "varies jointly" relationship can be expressed by ...

  y = kxz

We can find k from the given values.

  40 = k(10)(9)

  40/90 = k = 4/9 . . . divide by the coefficient of k

Now we want to find z for given values of x and y. That can be found from ...

  y = (4/9)xz

  9y/(4x) = z . . . . . multiply by 9/(4x)

Filling in the new numbers, we have ...

  z = 9·105/(4·55)

  z = 4 13/44 = 189/44 ≈ 4.2954...(repeating 54)