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
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
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.)