+50 In what bases, b, does (b + 10) divide into (8b + 10) without any remainder?
+118609 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?
+118609 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.
-------------
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
\(\frac{8b+10}{b+10}_{base\;10}=\frac{8*4+10}{4+10}_{base\;10}=\frac{42}{14}_{base\;10}=3_{Any\;base\;4\; or\; more }\)
