We say that three positive integers $a$, $b$ and $c$ form a family if the following two conditions are satisfied: $a + b + c = 900$. There exists an integer $n$, with $n \geqslant 2$, such that $$\frac{a}{n-1}=\frac{b}{n}=\frac{c}{n+1}.$$ Determine the number of such families.