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20000 people in town. X % on-leggd, half barefoot. How many sandals are worn in town?

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1 Answer

Let x = the fraction that are one-legged
 
x*20000 are one-legged and wear one sandal
0.5(1-x)*20000 go bare foot
0.5(100-x)*20000 wear two sandals
 
Let S = the number of sandals worn in town:
 
S = (1 sandal)(20,000)x + (0 sandals)(0.5)(1-x)(20,000) + (2 sandals)(0.5)(1-x)(20,000)
 
S = 20,000x + 0 + 20,000 - 20,000x
 
S = 20,000 sandals, or one per citizen
 
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You can actually figure this out logically.  X% of the people wear one sandal.  Of the remaining people, half wear no sandals, half wear two; so it averages to one sandal per person, just like the x%.  So the number of sandals equals the number of people.