If and are positive integers, find A*B given that

(AB)_9 + A_9 = B0_9

Express your answer in base 10 (you do not need to include the subscript).

Guest Oct 5, 2018

#1**+1 **

A and B must be integers in the range 0 to 8 (I'll assume here that A and B are both non-zero)

AB_9 is 9A+B

B0_9 is 9*B+0

So 9A+B + A = 9B + 0 or 10A = 8B

The only combination of integers in the range 1 to 8 that satisfy the above equality is A = 4 and B = 5, so A*B = 20 (in base 10).

Alan Oct 5, 2018