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# John surveyed a group of people about their knowledge of rats. To the nearest tenth of a percent, he found that 86.8% of the people

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John surveyed a group of people about their knowledge of rats. To the nearest tenth of a percent, he found that 86.8% of the people surveyed thought rats carried diseases. Of the people who thought rats carried diseases, 45.7% said that rats frequently carried rabies. Since rats do not frequently carry rabies, these 21 people were mistaken. How many total people did John survey?

Oct 11, 2018

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Let the num of people John surveyed  =  p

Let the num of people who thought rats carried diseases  =  d

Let the num of people who said rats carry rabies   =  r

86.8% of the people surveyed thought rats carried diseases. In other words...

the num of people who thought rats carried diseases  =  86.8% of the num of people John surveyed

d  =  86.8% of  p

d  =  86.8%  *  p

d  =  86.8/100  *  p

d  =  0.868p

45.7% of the people who thought rats carried diseases said that rats frequently carried rabies.

r  =  45.7% of d

r  =  0.457d

Since rats do not frequently carry rabies, these 21 people were mistaken. So we know that the num of people who said rats carry rabies is 21. So we know  r = 21

r  =  0.457d                  We know  r  =  21 ,  so we can substitute  21  in for  r .

21  =  0.457d                And we know  d = 0.868p , so we can substitute  0.868p  in for  d .

21  =  0.457(0.868p)    Now we just have to solve this equation for  p .

21  =  0.396676p

21 / 0.396676  =  p

52.93993  ≈  p

John surveyed a total of  53  people.

Oct 11, 2018