Check my answers , please ? algebra : inverse & directly

if y varies inversely as x, and y = 27 when x = 4, find y when x = 12.

my answer : 3

if y varies directly as x, and y = 27 when x = 4, find y when x = 12.

my answer : 81

y varies inversely as x means y=k(1/x) where k is a constant
so 27=k(1/4), so k=108.
now y=k/x=108/12=9 , y=9---------answer (1)

if y varies directly asx means y=k(x) , k is a constant
27=4 k, k=27/4
so y=(12)27/4=81, y=81 ----------------answer (2)