If the relation between the number of revolutions made by a tire and the radius of the tire varies inversely, then, you can write:
[tex]y=\frac{k}{x}[/tex]
where y is the number of revolutions, x the radius and k the constant of proportionality.
Based on the given information, you can calculate the value of k, as follow:
If x = 12 (radius in inches) and y = 100 (revolutions), then, by solving for k, you get:
[tex]k=yx=(100)(12)=1200[/tex]
Then, the relation between x and y can be written as follow:
[tex]y=\frac{1200}{x}[/tex]
Now, if the radius of the tire is x = 16, then, the number of revolutions to travel the same distance is:
[tex]y=\frac{1200}{16}=75[/tex]
In this case, the defined variables are:
x: radius of the tire
y: number of revolutions of the tire
k: constant variation = 1200
