let's say the diameter of the larger gear is "x".
the small one has a diameter of 16cm, we know that, this is 2.5 more than (1/4)x.
[tex]\bf 16=\cfrac{1}{4}x+2.5\implies 16-2.5=\cfrac{x}{4}\implies 13.5=\cfrac{x}{4}\implies 4(13.5)=x
\\\\\\
54=x[/tex]
