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Question-107122

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Question Number 107122 by aurpeyz last updated on 08/Aug/20
Answered by 1549442205PVT last updated on 09/Aug/20
Denote a,b,c be number of persons get medal in only one category dance,dramatics,music respectively m−be number of persons got exactly medal in two categories dance and dramatics n−in two categories dance and music p−in two categories dramatics and music Then from the hypothesis we have: { ((a+b+c+m+n+p+4=45(1))),((a+m+n+4=36 (2))),((b+m+p+4=12 (3))),((c+n+p+4=18 (4))) :} Adding up three equations (2)(3)(4) and simplification we get a+b+c+2(m+n+p)=54(5) from (1)we have a+b+c+m+n+p=41(6) Substracting (6) from (5) we get m+n+p=13 which is realy number of persons got exactly medals in two categories.Thus,we choose answer D:13
Denotea,b,cbenumberofpersonsgetmedalinonlyonecategorydance,dramatics,musicrespectivelym−benumberofpersonsgotexactlymedalintwocategoriesdanceanddramaticsn−intwocategoriesdanceandmusicp−intwocategoriesdramaticsandmusicThenfromthehypothesiswehave:{a+b+c+m+n+p+4=45(1)a+m+n+4=36(2)b+m+p+4=12(3)c+n+p+4=18(4)Addingupthreeequations(2)(3)(4)andsimplificationwegeta+b+c+2(m+n+p)=54(5)from(1)wehavea+b+c+m+n+p=41(6)Substracting(6)from(5)wegetm+n+p=13whichisrealynumberofpersonsgotexactlymedalsintwocategories.Thus,wechooseanswerD:13

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