Question 202687: A survey of residents in a small town showed the following:
25 ate beef 13 ate both beef and fish 9 ate all types
28 ate fish 14 ate both fish and poultry 7 ate none of them
30 ate poultry 15 ate both beef and poultry
Draw a Venn diagram. Label your diagram clearly.
Use your diagram to answer the following questions:
(a) How many ate fish, but not poultry or beef?
(b) How many ate poultry and fish, but not beef?
(c) How many ate only beef?
(d) How many ate nothing or only poultry?
I do not understand how to do word problems like this... This confuses me and I have tried to do this even my dad tried to help me but he confuses me more. lol.. Please help...
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! 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'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.
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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
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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
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Once you have all of this information, draw the venn diagram and fill in the appropriate regions to get:
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.
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