smc

Working from right to left, we see that $2-b=3$. Clearly if $b$ is a single digit integer, this cannot be possible. Therefore, there must be some borrowing from $a$. Borrow $1$ from the digit $a$, and you get $12-b=3$, giving $b=9$. Since $1$ was borrowed from $a$, we have from the tens column $(a-1)-8=7$. Again for single digit integers this will not work. Again, borrow $1$ from $7$, giving $10+(a-1)-8=7$. Solving for $a$: $10+a-1-8=7$ $1+a=7$ $a=6$ Finally, since $1$ was borrowed from the hundreds column, we have $7-1-4=c$, giving $c=2$. As a check, the problem is $762-489=273$, which is a true sentence. The desired quantity is $a+b+c=6+9+2=17$, and the answer is $\boxed{17}$.