## 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?​

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

1. 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