Find the absolute value of the difference of single-digit integers A and B such that
ABA_6 + 411_6 = 1215_6
Express your answer in base 6.
Although there are other ways to do this, I would start by converting the two right values to base ten.
The now converted equation is:
If we then subtract 151 from both sides, we get:
We can then use the equation 36A+6B+A=148, which simplifies to
The only non-extraneous values that work for this equation are A=4 and B=0
4-0=4, which makes the answer 4.