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.