The sum of two three-digit numbers is 711 in a certain base system, which is not more than 10,and the second digit from the right of each number is zero. The difference between these numbers is 75 in the base system. What is the product of these two numbers in the same base system?
My understanding( what I know)
In base $10$ numbers included can be 0-9.
In base $9$ numbers included can be 0-8
In base $8$ numbers included can be 0-7.
There will be two equation
$A+B=711$
$A-B=75$
where $A$ and $B$ are two three digit numbers.
On addition in base $8$, I got $2A=1006$. Now $A=403$ in base $8$? How? I understood the addtion part