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A recent survey of mathematicians and chess players found that 50% of mathematicians surveyed are chess players, and 20% of chess players surveyed are mathematicians. If N% is the percent of those surveyed who are both mathematicians and chess players, find N to the nearest whole number.

 Dec 2, 2023
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Let x represent the percent of people surveyed who are mathematicians, and let y represent the percent of people surveyed who are chess players. Since 50% of mathematicians surveyed are chess players, we have that 0.5x=y.

 

ince 20% of chess players surveyed are mathematicians, we have that 0.2y=x. Solving for x and y, we get that x=0.4 and y=0.2.

 

The percent of people surveyed who are both mathematicians and chess players is the product of the percent who are mathematicians and the percent who are chess players, so N=0.4⋅0.2=0.08=8​ to the nearest whole number.

 Dec 2, 2023

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