Minimum Value of Age c

Average age = 32 $\Rightarrow a + b + c = 96$. Given $b = a + 6$. To minimize $c$, we maximize $b$ (and thus $a$). Since $b \le c \Rightarrow a + 6 \le c$. $a + (a + 6) + c = 96 \Rightarrow 2a + 6 + c = 96 \Rightarrow 2a + c = 90$. Since $a + 6 \le c \Rightarrow 2a + a + 6 \le 90 \Rightarrow 3a \le 84 \Rightarrow a \le 28$. Max $a = 28 \Rightarrow b = 34$. Min $c = 96 - 28 - 34 = 34$ years.