## 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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Math
23 mins
2021-10-14T02:49:42+00:00
2021-10-14T02:49:42+00:00 1 Answer
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## Answers ( )

a.

15students are members of both clubsb.

50students only are members of the mathematics clubc.

25students only are members of the physics clubStep-by-step explanation:The given is:

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 clubLearn more:You can learn more about word problems in brainly.com/question/8907574

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