<PRE><B>Question 198483</B>
Starting from the fact that 9 people ate all types, we know that since 13 ate both beef AND fish, this means that 13 - 9 = 4 people ate both beef AND fish but NOT poultry.



Also, we know that 14 ate both fish AND poultry. So, this means that 14 - 9 = 5 people ate both fish AND poultry but NOT beef.




Furthermore, we&#39;re told that 15 people at both beef AND poultry. So 15 - 9 = 6 people ate both beef AND poultry but NOT fish.




Now to find out how many people ate ONLY beef, simply subtract the number of people ate beef and other products from the number of people who ate beef like this: 



People who ONLY ate beef = People who ate beef - people who ate beef AND fish - people who ate beef AND poultry - people who ate all three



People who ONLY ate beef = 25 - 4 - 6 - 9 = 6



So 6 people ONLY ate beef.


----------------------

Do the same with people who ONLY ate fish:


People who ONLY ate fish = People who ate fish - people who ate beef AND fish - people who ate fish AND poultry - people who ate all three



People who ONLY ate fish = 28 - 4 - 5 - 9 = 10



So 10 people ONLY ate fish



Finally, apply the same technique to find the number of people who ONLY ate poultry


----------------------


People who ONLY ate poultry = People who ate poultry - people who ate beef AND poultry - people who ate fish AND poultry - people who ate all three



People who ONLY ate poultry = 30 - 6 - 5 - 9 = 10




So 10 people ONLY ate poultry

----------------------

Once you have all of this information, draw the venn diagram and fill in the appropriate regions to get:



&lt;img src=&quot;http://i150.photobucket.com/albums/s91/jim_thompson5910/11.png&quot;&gt;





The following answers will use the Venn diagram:


a)


Number of people who ate fish, but not poultry or beef = number of people who ONLY ate fish



Number of people who ate fish, but not poultry or beef = 10



So there were 10 people who ate fish, but not poultry or beef 


b)


Number of people who ate poultry and fish, but not beef = number of people who ate both poultry AND fish (but not all three)


Number of people who ate poultry and fish, but not beef = 5



c)


Number of people who ate ONLY beef = 6


d)



Number of people who ate nothing or only poultry = number of people who ate nothing + number of people who ate poultry



Number of people who ate nothing or only poultry = 7 + 10 = 17



So there were 17 people who ate nothing or only poultry</PRE>