Question 1202602: In the correctly solved addition problem below, A and B represent digits. what is the value of A/B if AB+AAB = 844
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52864)   (Show Source):
You can put this solution on YOUR website! .
Looking on the ones digit, B, you see that there are only two possibilities for B:
B = 2 or B = 7.
But B= 7 does not work: otherwise, an odd digit would be the "tens" digit in the sum "844", which is not the case.
So, we accept B= 2 for a while.
Then we see that A= 7 works.
So, our digits are A= 7, B= 2.
It gives us the ANSWER:  =  .
Solved.
Answer by greenestamps(13206)  (Show Source):
You can put this solution on YOUR website!
AB
+ AAB
----
844
In the units column, B+B gives digit 4 in the sum, so B must be either 2 or 7.
In the tens column, A+A gives the even digit 4 in the sum, so there is no "carry" from the units column to the tens column. So B has to be 2.
A2
+ AA2
----
844
We can ignore the units column now. In the other columns we have
A
+ AA
---
84
Again we have A+A yielding digit 4 in the sum, so again A is either 2 or 7. But it has to be 7 in order to get leading digit 8 in the sum.
So A is 7 and we have
72
+ 772
----
844
ANSWER: A/B = 7/2
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