SOLUTION: In the correctly solved addition problem below, A and B represent digits. what is the value of A/B if AB+AAB = 844

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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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