Swap, Swap, Swap

Algebra Level 3

Let A & B be the 2-digit numbers, where A+B = 120.

If we swap the digits in A (call it A'), A' = A - B.

If we swap the digits in B (call it B'), A - B' = the sum of all digits of A & B.

And A' + B' = 3(B + 1).

Find 100A+B.

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