Answer:
A = 4
B = 5
C = 9
ABC + ACB = CBA is then
459 + 495 = 954
Explanation:
Working with
ABC + ACB = BCA,
There seems to be no feasible solution, but upon checking online, the correct question was obtained to be
ABC + ACB = CBA,
where A, B and C represent different digits
A B C +
A C B
C B A
So, for the units column
C + B = A
or
C + B = 10 + A
For the tens column
There are four possibilities
B + C = B
OR
1 + B + C = B
OR
B + C = 10 + B
OR
1 + B + C = 10 + B
Checking the equations one at a time
- If B + C = B, then C = 0
If C = 0, then units column equation 1, C + B = A, will not work because A, B, and C must stand for three different digits and B ≠ A.
If C = 0, then units column equation 2, C + B = 10 + A, will not work because B must stand for a single digit, B ≠ 10 + A
Therefore, tens column equation 1, B + C = B is not valid.
- If 1 + B + C = B, then C = -1
C must be a positive integer.
Therefore, tens column equation 2, 1 + B + C = B is not valid.
- If B + C = 10 + B
C cannot be equal to 10, as it is given that C is a single digit number.
Therefore, tens column equation 3, B + C = 10 + B, is not valid.
- If 1 + B + C = 10 + B
C = 9
Hence, this is the valid equation.
Our equation becomes
A B 9 +
A 9 B
9 B A
For the hundred's column, there is only one possibility.
Hundred's column equation 1:
since C is an odd number, the equation for the hundred's column is:
1 + A + A = C
1 + A + A = 9
therefore, A = 4
Our equation becomes
4 B 9 +
4 9 B
9 B 4
Solve for B using units column equation 2:
C + B = 10 + A
9 + B = 10 + 4
B = 5
Our final equation is then
4 5 9 +
4 9 5
9 5 4
Hope this Helps!!!