Giải thích các bước giải:
Ta có :
$A=\dfrac{\overline{abc}}{a+b+c}$
$\to A=\dfrac{100a+10b+c}{a+b+c}$
$\to A=\dfrac{(a+b+c)+99a+9b}{a+b+c}$
$\to A=1+\dfrac{99a+9b}{a+b+c}$
$\to A\le 1+\dfrac{99a+9b}{a+b+0},c\ge 0$
$\to A\le 1+\dfrac{99a+9b}{a+b}$
$\to A\le 1+9+\dfrac{90a}{a+b}$
$\to A\le 1+9+\dfrac{90a}{a+0}$
$\to A\le 1+9+90=100$
Dấu = xảy ra khi $b=c=0, 0<a\le 9$