+0  
 
+1
80
4
avatar+836 

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

 Nov 23, 2018
 #1
avatar+3830 
+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+95884 
+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+95884 
+1

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

 

 

cool cool cool

 Nov 23, 2018
 #4
avatar+3830 
+1

Haha! Your explanation is still better! 

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

27 Online Users

avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.