+0  
 
0
129
4
avatar+50 

In what bases, b, does (b + 10) divide into (8b + 10) without any remainder?

 Feb 27, 2020
 #1
avatar
+1

b + 10 divides 8b + 10 for b = 4.

 Feb 27, 2020
 #2
avatar+109806 
+1

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?

 Feb 28, 2020
 #3
avatar+50 
+1

Base B

jamesbroadman  Feb 28, 2020
 #4
avatar+109806 
+1

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 laugh

If b=4 then you have

 

\(\frac{8b+10}{b+10}_{base\;10}=\frac{8*4+10}{4+10}_{base\;10}=\frac{42}{14}_{base\;10}=3_{Any\;base\;4\; or\; more }\)

Melody  Feb 28, 2020
edited by Melody  Feb 28, 2020

13 Online Users