If​ a, b, and c are digits for which the following​ holds, then a+b+c=​_____.

Thanks for the A2A. First, look at the last digit column. B only makes sense for 7, as 15-7 is 8. 

Also, look at the first digit column and you'll see that C is 5. 

If you add 588 and 297, the answer is 885, which means a is 8. 

7+5+8 = 20.

Cheers!