Of 55 students in the fifth grade, 43 are fans of the local basketball team and 35 are fans of the local hockey team. Twenty - three students are fans of both teams. How many students are fans of the hockey team but not the basketball team?
PS MY ANSWER IS 12
Right.
12 students
To find the number of students who are fans of the hockey team but not the basketball team, we need to subtract the number of students who are fans of both teams from the total number of students who are fans of the hockey team.
First, we know that there are 55 students in the fifth grade. So this is our total number of students.
Next, we know that 43 students are fans of the basketball team and 35 students are fans of the hockey team. However, we also know that 23 students are fans of both teams.
To find the number of students who are fans of the hockey team but not the basketball team, we can use the principle of inclusion-exclusion. We add the number of students who are fans of the basketball team to the number of students who are fans of the hockey team and then subtract the number of students who are fans of both teams:
43 (fans of basketball team) + 35 (fans of hockey team) - 23 (fans of both teams) = 55 (total number of students)
Now, let's solve for the number of students who are fans of the hockey team but not the basketball team:
35 (fans of hockey team) - 23 (fans of both teams) = 12 students
Therefore, there are 12 students who are fans of the hockey team but not the basketball team.