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For what base, \(b\), is \(14_b + 24_b = 41_b\) true?

 Nov 23, 2018
 #1
avatar+4330 
+2

We first translate this into an equation:

\(1*b^1+4*b^0+2*b^1+4*b^0=4*b^1+1*b^0\).

 

This is equal to \(b+4+2b+4=4b+1\).

 

Solving we get, \(3b+8=4b+1, b=7\).

 

Thus, the answer is base \(\boxed{7}.\)

.
 Nov 23, 2018
 #2
avatar+105238 
+2

So.....let b be the base.....and we have

 

(1b + 4)  + ( 2b +4)    = 4b + 1      simplify

 

3b + 8   = 4b + 1         subtract 3b, 1 from both sides

 

b = 7

 

Check

 

14+ 247 =  417

 

In base 10

 

11 + 18  = 29     ⇔   True!!!

 

 

 

cool cool cool

 Nov 23, 2018
 #3
avatar+105238 
+1

Heck.....tertre beat me to it.....LOL!!!

 

 

cool cool cool

 Nov 23, 2018
 #4
avatar+4330 
+1

Haha! Your explanation is still better! 

tertre  Nov 23, 2018
edited by tertre  Nov 23, 2018

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