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If A, B, and C are the digits of the base-five number ABC, which is equal to the base-10 number 47,what does digit B represent?

 Dec 26, 2018
 #1
avatar+7350 
+2

We can convert  47  base 10 into base 5. This probably isn't the best way to do it but this is the easiest for me...

 

 _     _     _

25    5     1

 

how many 25's fit into 47? just 1.

 

 1     _     _

25    5     1

 

47 - 25  =  22  so there is 22 left.

how many 5's fit into 22? 4.

 

 1     4     _

25    5     1

 

22 - 20  =  2  so there is 2 left.

how many 1's fit into 2? 2.

 

 1     4     2

25    5     1

 

47 base 10  =  142 base 5

 

B = 4

 Dec 26, 2018
 #2
avatar+98000 
+1

Maybe other ways to do this...but....

 

The largest that A can be is 1

 

47 - 1*5^2 =  

 

47 - 25 = 22

 

This implies that B = 4  because    4(5) = 20

 

And C = 2

 

4710   =   1425

 

So

 

B =  4

 

 

cool cool cool

 Dec 26, 2018
 #3
avatar+98000 
+1

Here's one more method :

 

47 / 5  =  9   Remainder  2

 

9 / 5  =   1 Remainder  4 

 

1 / 5 =   0 Remainder  1

 

Reading the red digits from bottom to top  gives us    1425

 

cool cool cool

 Dec 26, 2018

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