The variable z is proportional to x and inversely proportional to y. When x is 12 and y is 4, z has the value 57 what is the value if z when x=18 and y=10

Giiven Z is proportional to x let us suppose Z contain x as Cx where c is some constant

Z is inversely proportional to y let us suppose Z contain y as k (1/y) where k is also some another constant.

WE can write Z = (c x) / (ky)

Or Z = (c/k) (x/y) where c/k is a constant

Given at x = 12 y = 4 z = 57. let us place these values in this equation

57 = (c/k) (12/4)

57 = (c/k) (3)

19 = c/k we got the constant value.

we can write Z = 19 (x/y)

Now if x = 18 and y = 10 we need to find Z

Z = 19 (18/10)

Z=34.2

Answer : 34.2