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The following addition problem is not correct if the numbers are interpreted as base 10 numbers. in what number base is the problem correct?

66+87+85+48

 Aug 22, 2022
 #1
avatar+2446 
0

that's not a problem...

 Aug 22, 2022
 #2
avatar
0

sorry. 

The following addition problem is not correct if the numbers are interpreted as base 10 numbers. in what number base is the problem correct?

66+87+85+48=132

 Aug 22, 2022
 #3
avatar+2446 
0

Let the base be b. Off the bat, we know that \(b>8\).

 

If we added everything, it would look something like this:

 

        66

        87 

+      85

        48 

\(\overline{\color{white}{wwwwww}}\)

       132

 

Adding up the ones digit gives us 26, so we have \(26 \mod b = 2\)

 

The only options for b are b = 12 or 24. 

 

If b = 12, the sum of the ones digit would be \(22_{12}\), so we could carry the 2 to the tens column. Adding everything up would give us \({24}_{12}\), so our answer would be \(242_{12}\).

 

This means that the base is \(\color{brown}\boxed{24}\).

 

(Add it up to see for yourself.)

 Aug 23, 2022
 #4
avatar+33151 
+1

You could also look at it like this:

 

 Aug 23, 2022

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