Define the maximal value of the ratio of a three-digit number to the sum of its digits. Let the three-digit number be represented as $abc$, where $a$, $b$, and $c$ are digits, and $a \neq 0$. The problem requires finding the maximum of $\frac{100a + 10b + c}{a + b + c}$.

Let's think step by step and output the final answer within \boxed{}.
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