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

Guest Aug 22, 2022

#2**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

Guest Aug 22, 2022

#3**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.)

BuilderBoi Aug 23, 2022