Question 170328: This isn't exactly algebra, but i need help:
Grandma Harris is going to host a huge family gathering on Thanksgiving Day. She has 8 grandkids and his year Grandma has decided that they will all help with the serving or clean up. The kitchen is small so she must select 4 kids to wash dishes after the meal. The others will help with the serving during the meal. The selection is not an easy matter, however, for there are attachments among the children that prevent a free choice of 4 dishwashers. Can you help grandma select a dishwashing crew of 4 to satisfy all these whims?
-Mark will work with anybody.
-Rafi won't wash dishes unless Adena helps too.
-Adena won't work without Jenny.
-Adam won't work without Ashley.
-Jenny will work with anybody.
-Daniel won't wash dishes with Adam unless Liz helps too, and won't work with Adena unless Adam also helps.
-Liz won't work with both Rafi and Adena and won't wash dishes with either Mark or Jenny.
-Ashley won't help unless either Rafi or Daniel wash dishes and won't work with Adena unless Liz works too, and won't work with both Mark or Jenny.
Answer by Mathtut(3670)   (Show Source):
You can put this solution on YOUR website! I am going to label the statements to make this easier
1. Mark will work with anybody
2. Rafi wont wash dishes unless Adena helps too.
3. Adena wont work without Jenny
4. Adam wont work without ashley
5. Jenny will work with anybody
6. a)Daniel wont wash dishes with adam unless liz helps too. b)Daniel wont work
with Adena unless Adam also helps.
7. a)Liz wont work with both Rafi and Adena. b)Liz wont wash dishes with either
mark or jenny
8. a) Ashley wont help unless either Rafi or Daniel wash dishes. b) Ashley wont
work with Adena unless liz works too. c) Ashley wont work with both mark Jenny (I personally think it should say "and" not "or" but it appears to not make a difference in this problem
:
Because of statement 3 and 4 we have the beginnings of two groups which we will call #1 and #2....#1 composed of Adam and Ashley and #2 composed of Adena and Jenny.
:
Lets deal with Daniel. Daniel cannot be part of group #2 because of statement 6b.......the reason this is true is because Adam and Adena will not work together because of statement 8b. In other words if Adam and Adena worked together we would have to join group #1 and group #2 together and because of 8b that would put 5 people in one group......conclusion is Daniel has to be in group #1.
:
so now we have group #1 with Daniel, Adam, and Ashley. Group #2 is composed of Adena and Jenny.
:
We now have 2 scenarios:
:
Scenario #1
:
group #1 Daniel,Adam,and Ashley as Dish washers....if this is true then Liz must join them because of 6a which states that Daniel wont wash dishes with Adam unless Liz helps. Therefore group #2 composed of Adena, Jenny, Rafi, and Mark. If you read each statement carefully no statements seem to reject this scenario........conclusion Dishwashers under this scenaro are Daniel,Adam,Ashley,and Liz.
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Scenario #2
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under this scenario we make the opposite assumption that Group #1 are servers. If this is true then Rafi must join group #2 and be a dishwasher because of statement 7a which states that either Daniel or Rafi have to wash dishes. That leaves Liz and Mark to deal with in this scenario. But because of statement 7a, which states that Liz will not work with both Rafi and Adeana, Liz has to go into group #1 under this scenario. Which leaves Mark to complete group #2.
Believe it or not these groups are composed of the same people as scenaro 1 only the jobs have changed. Again in this scenario it appears that no statements reject this scenario. meaning the dishwashers are Adena, Jenny,Rafi, and Mark.
:
Final conclusion is that either group #1 or group # 2 can wash dishes. final group #1 being (Daniel,Adam,Ashley,and Liz) or group #2 composed of (Adena, Jenny,Rafi, and Mark.)
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