of 100 students,65 are members of a mathematics club and 40 are members of a physics club. if 10 are members of neither club then how many s

Question

of 100 students,65 are members of a mathematics club and 40 are members of a physics club. if 10 are members of neither club then how many students are members of
a.both clubs?
b.only mathematics club?
c.only physics club?​

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Sophia 23 mins 2021-10-14T02:49:42+00:00 1 Answer 0

Answers ( )

    0
    2021-10-14T02:50:58+00:00

    a. 15 students are members of both clubs

    b. 50 students only are members of the mathematics club

    c. 25 students only are members of the physics club

    Step-by-step explanation:

    The given is:

    • There are 100 students
    • 65 are members of a mathematics club
    • 40 are members of a physics club
    • 10 are members of neither club

    We need to find how many students are members of

    a. both clubs?

    b. only mathematics club

    c. only physics club

    ∵ The total number of students = 100

    ∵ 10 are members of neither club

    – Subtract 10 from 100 to find the members of the mathematics

      club or the physics club

    ∵ 100 – 10 = 90

    ∴ There are 90 members of the mathematics club or physics club

    ∴ n(mathematics or physics) = 90

    ∵ 65 students are members of a mathematics club

    ∵ n(mathematics) = 65

    ∵ 40 students are members of a physics club

    ∴ n(physics) = 40

    ∵ n(mathematics or physics) = n(mathematics) + n(physics) – n(both)

    ∴ 90 = 65 + 40 – n(both)

    ∴ 90 = 105 – n(both)

    – Add n(both) to each side

    ∴ n(both) + 90 = 105

    – Subtract 90 from each side

    ∴ n(both) = 15

    ∴ 15 students are members of both clubs

    a. 15 students are members of both clubs

    ∵ 65 students are members of the mathematics club

    ∵ 15 of them are members of the physics club

    ∴ n(mathematics only) = 65 – 15 = 50

    ∴ 50 students only are members of the mathematics club

    b. 50 students only are members of the mathematics club

    ∵ 40 students are members of the physics club

    ∵ 15 of them are members of the mathematics club

    ∴ n(physics only) = 40 – 15 = 25

    ∴ 25 students only are members of the physics club

    c. 25 students only are members of the physics club

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