Please solve in a diagrammed manner:
Dear Student,
We have:
8 A
+ 8 B
_____
C B 3
Since A, B and C are digits, they can only take values 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9.
So, the minimum value of the sum above is 80 + 80 = 160 and the maximum value is 89 + 89 = 178. Thus, C = 1.
8 A
+ 8 B
_____
1 B 3
Now, B can either be equal to 6 or 7.
Let us assume that B = 6. Then the final sum is 163. Here, the only two numbers which add up to 163 are 82 and 81. So, 82 + 81 = 163, which gives B = 2 or 1, which is a contradiction since we had assumed B to be 6. Thus, the final sum must be 173. This gives B = 7.
So,
8 A
+ 8 7
_____
1 7 3
Now, 87 + 86 = 173, which gives A = 6.
Thus,
8 6
+ 8 7
_____
1 7 3
We have:
8 A
+ 8 B
_____
C B 3
Since A, B and C are digits, they can only take values 0, 1, 2, 3, 4, 5, 6, 7, 8 or 9.
So, the minimum value of the sum above is 80 + 80 = 160 and the maximum value is 89 + 89 = 178. Thus, C = 1.
8 A
+ 8 B
_____
1 B 3
Now, B can either be equal to 6 or 7.
Let us assume that B = 6. Then the final sum is 163. Here, the only two numbers which add up to 163 are 82 and 81. So, 82 + 81 = 163, which gives B = 2 or 1, which is a contradiction since we had assumed B to be 6. Thus, the final sum must be 173. This gives B = 7.
So,
8 A
+ 8 7
_____
1 7 3
Now, 87 + 86 = 173, which gives A = 6.
Thus,
8 6
+ 8 7
_____
1 7 3