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110 members of a sports club play atleast one of the games, football, basketball and volleyball. If 20 play football and basketball only, 15 play football and volleyball only, 26 play basketball and volleyball only, x play all the three games, 2x each play only one game, how many play basketball altogether?

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14 answers

  1. Let the Sports Club be denoted by U,
    .
    F = Football
    .
    B = Basketball
    .
    V = Volleyball
    .
    n(U) = 110
    .
    n(FnBnC') = 20
    .
    n(FnVnB') = 15
    .
    n(BnVnF') = 26
    .
    n(FnBnV) = x
    .
    n(FnB'nV') = n(F'nBnV') = (F'nB'nV) = 2x
    .

    Note: B', F' and V' denote the complements of the various sets(clubs).
    .
    n(U) = n(FuBuV) + n(FuBuV)'
    .
    In this case, n(FuBuV)' is empty.
    .
    110 = 2x + 20 + x + 15 + 2x + 26 + 2x
    .
    110 = 61 + 7x
    .
    49 = 7x
    .
    x = 7
    .
    n(B) = 20 + 26 + x + 2x
    .
    n(B) = 20 + 26 + 3x
    .
    n(B) = 20 + 26 + 21
    .
    n(B) = 67
    .
    67 members play Basketball altogether.

    ~Darematics(07034495462)

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  2. i need answer

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  3. Pls Ayodeji And Edidiong Umanah How Did U Get 52 To Be The Answer

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  4. 52 is the answer

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  5. Pls how was the answer 52 gotten

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  6. 52

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  7. 67 members play basketball altogether

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  8. How many played football and how many played volleyball. Please I need a straight answer

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  9. pls how did you get 52

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  10. Pls how was 52 gotten

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  11. Thank you so much
    Have been trying it all day but still didn't get

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  12. Pls can u represent in on a venn diagram

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  13. How did you arrive at 52

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  14. Pls can u represent it in a Venn diagram

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