Evil Percentage Problem
You are at a conference attended by mathematicians and philosophers. Your spies told you that 20% of the mathematicians and 40% of the philosophers attending are evil. After some observation, you conclude that there are 2 evil philosophers present, and 25% of the total number of people present are are evil. How many evil mathematicians are attending the conference?
The answer is 3.
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You know that there are 2 evil philosophers, which make up 40% of the total philosopher. That means that 60% are not evil. This means that there are 5 total philosophers. Call e the number of evil mathematicians. 20% of the mathematicians are evil, which is the same as 5 1 of the total mathematicians. 5 1 = e, so total number of mathematicians = 5e. 25% of the total people present are evil. So create the following equation. 5 + 5 e 2 + e = 1 0 0 2 5 . 2+e is the 2 evil philosophers + the evil mathematicians. 5 is the total philosophers + the 5e evil mathematicians. Solve by multiplying both sides by 100. 200 + 100e = 125 + 125e -> 25e = 75 -> e = 3 -> There are 3 evil mathematicians at the conference.