A performing magician has a disappearing act where he makes a random member of his audience disappear and reappear. Unfortunately, one-tenth of the time, the audience member never reappears. However, one-fifth of the time, two people reappear instead of only one. If the magician has put on 100 performances of the act this year, how many people have reappeared?
How many times has no one reappeared? ** One-tenth of the time, no one reappears, so there have been 100 / 10 = <<100/10=10>>10 times no one has reappeared.
How many times have 2 people reappeared? ** One-fifth of the time, two people reappear, so there have been 100 / 5 = <<100/5=20>>20 times 2 people have reappeared.
How many people have reappeared in all? ** In those 20 times, 2 * 20 = <<2*20=40>>40 people have reappeared in all.
How many times has one person reappeared? ** Thus, there have been 100 - 10 - 20 = <<100-10-20=70>>70 times one person has reappeared.
How many people have reappeared in all? ** Therefore, over 100 acts, 70 + 40 = 100 people have reappeared in all.
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