Suppose that y varies directly with x and inversely with z, and y = 20 when x = 15 and z = 3. write the equation that models the relationship. then find y when x = 6 and z = 6.

y = 4x/z , y = 4.

Step-by-step explanation:

Recall ; from Variation,

y ∞ x 1

y ∞ ¹/z 2

Now , combine equation 1 & 2 together, it metamorphosed to

y  =  kx/z 3

Remember, k is a constant and the value  must be find first

K = yz/x

  = (20 x 3) /15

  = 4

 To get the equation that models the relationship, we substitute for k in equation 3

y = 4x/z.

To find the value of y , substitute for the values of k, x and z

y = ( 4 x 6 )/6

  = ²⁴/₆

 = 4