math

in city high school,the marching band has 48 members and the orchestra has 36 member.if there are only 12 students who belong to only one group and all students belong to at least one group how many students belong to both group?

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  1. Let x be the number of student who belongs to both groups; y, belongs to
    the band only; z, belongs to the orchestra only. Then
    x+y=48---------(1)
    x+z=36---------(2)
    y+z=12---------(3)
    (2)-(3)=>
    x-y=24----------(4)
    (1)+(4)=>
    2x=72=>
    x=36

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    bobpursley

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