The variable z is directly proportional to x, and inversely proportional to y. when x is 10 and y is 4, z has the value 47.5.

what is the value of z when x = 13, and y = 10

Because Z is directly proportional to X and inversely proportional to Y, therefore


When X=10 and Y=4, Z=47.5.
Therefore
k(10/4) = 47.5
   2.5k = 47.5
        k = 19.

That is,


When X=13 and Y=10, obtain
Z = (19*13)/10 = 24.7

24.7