Question

Z is partly constant and partly varies directly with x and inversely with y.z=10 when x=4 and y=8&z=4when x=12 y=6 find z when x=20and y=4

Answer 1

z = k x / y + c

10 = k (4) / (8) + c
4 = k(12) / (6) + c

80 = 4 k + 8 c
24 = 12 k + 6 c

240 = 12 k + 24 c
24 = 12 k + 6 c
----------------------------
216 = 18 c
c = 12
24 = 12 k + 72
k = - 4
so
z = -4 (x / y) +12
now put in (20,4)
z = -4 ( 5) + 12
check my arithmetic :)

Answer 2

z is partly constant and partly varies directly with x and inversely with y: z = c + mx/y
So plug in your numbers to get
4/8 m + c = 10
12/6 m + c = 4
Now solve for m and c, and then find z(4,20)

Answer 3

Yes