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?
Accepted Solution
A:
a. 15 students are members of both clubsb. 50 students only are members of the mathematics clubc. 25 students only are members of the physics clubStep-by-step explanation:The given is:There are 100 students65 are members of a mathematics club40 are members of a physics club10 are members of neither clubWe need to find how many students are members ofa. both clubs?b. only mathematics clubc. 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 clubsa. 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 clubb. 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 clubc. 25 students only are members of the physics clubLearn more:You can learn more about word problems in brainly.com/question/8907574#LearnwithBrainly