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Let  b  be the base. Then convert all the numbers in the equation to base ten to get:

 

1b + 1   +   1   =   1b² + 0b + 0

 

b + 2   =   b²

 

0   =   b² - b - 2

 

0   =   (b + 1)(b - 2)

 

b  =  -1     or     b  =  2

 

Reject the negative solution, so  b = 2

 

We can check this answer by counting in base 2:

 

0

1

10

11            ←   Adding  1  more to 11

100          ←   gives us  100

101

110

111

1000

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