Question 642420: A, B, C each represent a different number between 1 and 9. What do A, B, and C represent in the following addition problem ... please show work my email address is b.dankbar@comcast.net
AA
BB
+ CC
_______
= ABC
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The addition of the ones column shows
A+B+C=10n+C with n being the number carried over (0, 1, or 2),
so A+B=10n
The only option is n=1, because two numbers between 1 and 9 cannot add to zero, and cannot add to 20 either.
The addition of the tens column (with the 1 carried over) shows
A+B+C+1=AB , meaning A+B+C+1=10A+B
Subtracting A and B from both sides we get
A+B+C+1-A-B=10A+B-A-B ---> C+1=9A
The only option is A=1, because A=2 would require C+1=18.
With A=1,
C+1=9A=9
C+1=9 ---> C=8
A+B=10, with A=1 means
1+B=10 ---> B=9
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