Solving variation equations

Question

The quantity Z varies jointly with x and y and inversely with w When x=11, y= -7 and w = -7, z=-99 Find Z when x=3, y=4 and w=2/

 

Answer 1

Z = kxy / w

-99 = k(11)(-7) / (-7) So, k = -9.

Z = -9xy / w

When x = 3, y = 4, and w = 2, Z = -9(3)(4) / 2 = -54

Answer 2

From description:

z(x,y,w) = kxy/w

-99 = k(11)(-7)/-7 = 11k

k = -9

z(x,y,w) = -9xy/w

z(3,4,2) = -9(3)(4)/2 = -54

Answer 3

z = kxy/w

-99= k(11)(-7)/-7 = 11k

k = -99/11 = -9= the constant of proportionality

k-9

z= -9xy/w

z = -9(3)(4)/2 = -54

z=-54 when x=3, y=4 and w=2