In this correct addition of two 2-digit numbers, A and B represent different digits. Find the value of A. AB + AA = 1B2

Question

Find the value of the unknown in the addition problem.

Answer 1

Hi Shareeka,

Looking at only the units places of your equation, (A+B) must be either 2 or 12. Using the tens places, then (A+A) is either B+10 or (B-1)+10 if there was a 1 carry-over from the units addition.

If A+B =2, then both A and B ≤ 2 and the tens places would not have an addition carry-over to make the 1 in the hundreds place.

So now A+B=12 and A+A = (B-1)+10.

Substituting B=(12-A) from the first equation,the second equation becomes 2A=(12-A)-1+10.  3A=21 and A=7. Then B=12-7=5.

Checking the addition using these digits gives 75+77 = 152.

152 matches 1B2 when B=5.