1.

Find the solution of AA+BB+CC=ABC find the value of ABC

Answer»

First focus on the answer ABC. Notice the largest result can be 99 + 88 + 77 = 264, so the answer has to be in the 200s or the 100s. This means A = 1 or 2.

Next focus on the sum of the units digits. We know A + B + C = C (units), which means A + B = 0 (units).

Therefore, we have A = 1 and B = 9 or A = 2 and B = 8. There are TWO possible cases:

11 + 99 + CC = 19C
22 + 88 + CC = 28C

In the second case, we have 110 + CC = 28C. Focusing on the TENS column, we must have 1 + C = 8, which means C = 7. But then we end up with 110 + 77 = 187, which cannot work since we need a 2 in the hundreds place. This case does not yield a result.

In the first case, we have 110 + CC = 19C. Focusing on the tens column, we must have 1 + C = 9, which means C = 8. We then have 110 + 88 = 198, and this works!

The answer is 11 + 99 + 88 = 198.


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