Base of Number

If the number 86 in base 10 is represented as 321 in base b, what is the base-ten representation of the number 123 in base b?
Source: NCTM Mathematics Teacher, November 2006

SOLUTION
3b^2+2b+1=86
3b^2+2b-85=0
Solving the quadratic equation for b yields b=5.
123_b=1\cdot 5^2+2\cdot 5+3
=25+10+3
=38_{10}

Answer: 38

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About mvtrinh

Retired high school math teacher.
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