Problem:
The knights in a certain kingdom come in two colors. of them are red, and the rest are blue. Furthermore, of the knights are magical, and the fraction of red knights who are magical is times the fraction of blue knights who are magical. What fraction of red knights are magical?
Answer Choices:
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B.
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E.
Solution:
Let be the number of knights: then the number of red knights is and the number of blue knights is .
Let b be the fraction of blue knights that are magical - then 2b is the fraction of red knights that are magical.
Thus we can write the equation = = = .
We want to find the fraction of red knights that are magical, which is
The problems on this page are the property of the MAA's American Mathematics Competitions