Please Help... z varies inversely with x and directly with y. When x = 6 and y = 2, z = 5. What is the value of z when x = 4 and y = 9?

z ∝ y/x
Then, z = ky/x where k is a non-zero constant.

x = 6 and y = 2, z = 5 :
(5) = k(2)/(6)
k = 15

Hence, z = 15y/x

when x = 4 and y = 9 :
z = 15(9)/4
z = 135/4

...... The answer is : C. 135/4

Thank you so much :)

z = k y / x
x z / y = k = 30 / 2 = 15

z = 15 x 9 / 4 = 135 / 4_____Option c

z varies inversely with x and directly with y
z = k y / x , where k is any constant

z=5; x=6; y=2
5 = k (2) / 6
5 = k / 3
k = 15

z = 15 y / x
when x=4 and y=9
z = 15 (9) / 4
z = 135/4 = 33.75