In what bases, b, does (b + 10) divide into (8b + 10) without any remainder?
Are those expressions in base b or in base 10?
If it is in base b then b=10 so b+10 = 2*b base b
and 8b+10 = 8b+b = 9b base b
But if the expressions are in base 10 then b+10 = 10+b base 10
and 8b+10 = 10+8b base 10
So which is it?
In what bases, b, does (b + 10) divide into (8b + 10) without any remainder?
Well if everything is in base b then we have
b+10=2b (any base)
8b+10=9b (any base)
9b/2b= 4.5
So I am reasonably sure there will be a remainder in any base.
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I suspect the tens in the question are actually meant to be in base 10
in which case guests answer of base 4 does work. Thanks guest for your answer
If b=4 then you have
8b+10b+10base10=8∗4+104+10base10=4214base10=3Anybase4ormore