How would you calculate the below ?

The results of surveying 100 residents of a city reported that 40 read the daily morning paper, 70 read the daily evening paper %26amp; 20 read neither. How many:


1. Read at least 1 paper?


2. Read both?


3. Read exactly one daily paper?





Please assist in how you would calculate the above.


Thank you.

How would you calculate the below ?
1. 100 - 20 = 80





2. 100 - (100 - 70) - (100 - 40) = 10





3. 80 - 10 = 70
Reply:out of 100, 20 people dont read any... so let us discount them... that leaves 80 people who read....





40 read morning paper %26amp; 70 read evening paper... that is a total of 110... but we saw that only 80 people are there to read....





so the extra 30 (110-80) must be the number of people who read both...





hence 10 (40-30) people read only morning paper; 40 (70-30)people read only evening paper; 30 people read both





======


it can be solved algebraically also.





let m be number of persons reading morning paper only


let e be number of persons reading evening paper only


let b be number of persons reading both paper





then m+b = 40 ... A


e+b = 70 .... B


m+e+b = 80 (excluding the 20 who dont read any) ....C





C-A gives that e = 40


C-B gives that m = 10


so b = 30





===========





the above problem can be represented graphically using the Venn Diagram
Reply:1. 80


2. 30


3. 50





people who read the morning paper:


30 read both


10 read morning only


----


40





people who read the evening paper:


30 read both


40 read evening only


----


70





total that read only one paper:


10 read morning only


40 read evening only


----


50
Reply:To get the first answer you simply need to subtract the number of people who don't read a paper at all from the number of people surveyed. This gives you the number of people who read at least one paper.





For the 2nd answer add up the number of people who read each paper and subtract the number of people who read at least one paper. That is the number of people that would have to read both.





For answer # 3, take the number of people who read both news papers and subtract it from the number of people who read at least one paper. That will give you the number of people who read 1 and only 1 paper.
Reply:OK--Since 20 out of 100 read neither paper, then obviously 80 must read at least one paper. Since only 80 read at least one (and maybe 2) and 110 report reading either the AM or PM version, obviously then 30 people must read both papers. Lastly, since 20 read no papers and 30 read both papers, then 50 must read only one paper. That's my solution
Reply:well 20 dont read either, so 80 read at least 1


40 read the morning/ 70 evening,


we only have 80 reading at all, so you end up with 30 reading both, and 50 reading exactly 1.


try to remember, you're dealing with 110 papers and only 80 people. ;)








and for the math teacher above me, 100 people were surveyed about 110 papers. ;)


good luck, took me a minute, hope i was right lol
Reply:let A be the no of morning reader , B the number of evening reader


then


a = 40


read atleast one = A (Union) B


read both = A (intersection) B


Exactly 1 = A(B bar) +(aBar)B


now use formulaAUB = A+B-a intersect b


etc


These formula are quite common in Elementary set Theory
Reply:100 people took the survey and 20 DON'T read the paper. That means 80 people had to have read the paper.





110 people read either the morning or evening paper


80 people actually read the paper (based on 20 NOT reading it)





That leaves us with 30. 30 people read BOTH the morning and evening paper.


Since 40 people total read the morning paper, that means 10 people just read the morning paper itself. 40 people read the evening paper.





So to answer your qestion:





80 people read at least 1 paper


30 people read both papers


50 people read exactly 1 paper.





(it helps if you make a Venn Diagram)
Reply:do your homework yourself


besides thats only common sense