3. The sum of the digits of a three-digit number is 18. The first digit is equal to one-eighth of the number formed by the other two digits, and the last digit is equal to one-eighth of the number formed by the first two digits. Calculate this number.

(8 points)
3. Let's denote the digits, for example, by $a, b, c$. According to the problem, we can write the first equation as $a+b+c=18$, the second as $a=\frac{1}{8}(10 b+c)$, and the third as $c=\frac{1}{8}(10 a+b)$. We rearrange the equations and get a system of three equations with three unknowns:

$a+b+c=18$,

$8 a-10 b-c=0$,

$-10 a-b+8 c=0$.

The solutions to the system are $a=6, b=4$, and $c=8$. The desired number is 648.

![](https://cdn.mathpix.com/cropped/2024_06_07_7bf3e9b12130e254269ag-07.jpg?height=211&width=1642&top_left_y=748&top_left_x=207)