If z varies inversely as w, and z=5 when w=8, find z when w=10

z=4. If z varies inversely as w, and z=5 when w=8, then when w=10 the value of z is 4.

This exercise is an example of  reverse proportionality, Two magnitudes a and b are inversely proportional when there is a constant k such that

a⋅b=k, where constant k is called the proportionality constant.

Then if z varies inversely as w, and z=5 when w=8

z.w=k > 5.8=k > k=40

So, let's find z when w = 10. With k = 40

z.w=K, clear z from the equation

z=k/w > z=40/10 > z=4