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