30.9k views
5 votes
All students in a class practice at least one of the following extracurricular activities: swimming and dancing, Three-fifths of the class's students practice swimming and three-fifths of students practice dance. Five students practice both extracurricular activities. How many students does the class have?​

User Carlita
by
7.6k points

1 Answer

1 vote

Final answer:

To find the total number of students in the class who practice swimming and dancing, we use the principle of inclusion-exclusion. The equation based on the given fractions of students participating in each activity and those participating in both leads us to conclude that the class has 25 students.

Step-by-step explanation:

The question involves solving a problem related to extracurricular activities among the students in a class. To find out the number of students in the class, we can use the principle of inclusion-exclusion. As per the problem statement:

  • Three-fifths of the class practices swimming.
  • Three-fifths of the class practices dance.
  • Five students practice both activities.

Let n be the total number of students in the class. Then, the number of students practicing each activity is (3/5)n, and the sum of the students practicing either swimming or dancing is 2*(3/5)n, but this double counts the students who do both. Therefore, we subtract the five students who do both to avoid double counting:

Total number of students = (3/5)n + (3/5)n - 5

However, since every student does at least one activity, the total number in this equation is just n. So,

n = (3/5)n + (3/5)n - 5

Simplifying the equation,

n = (6/5)n - 5

5 = (1/5)n

Therefore, n = 25. So, the class has 25 students.

User Sonichy
by
8.8k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories