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?
Thoughts? Step-by-step reasoning:
One - tenth of the time, no one reappears, so there have been 100 / 10 = 10 times no one has reappeared. One - fifth of the time, two people reappear, so there have been 100 / 5 = 20 times 2 people have reappeared. In those 20 times, 2 * 20 = 40 people have reappeared in all. Thus, there have been 100 - 10 - 20 = 70 times one person has reappeared. Therefore, over 100 acts, 70 + 40 = 100 people have reappeared in all.
Thus, the answer is 110.