At small town high there are 100 students,each of whom takes atleast one of Biology,Chemistry,or physics.There are 50 student in Biology,60 in chemistry,and 70 in Physics.If 24 students are enrolled in exactly two of the classes,how many students are in all three?
50+60+70-24-x = 100
Draw your Venn diagram to see why.
There are 204 students in all three
34
To find out how many students are enrolled in all three classes (Biology, Chemistry, and Physics), we can follow these steps:
1. Start by adding the number of students in each class: Biology (50), Chemistry (60), and Physics (70).
- Biology: 50 students
- Chemistry: 60 students
- Physics: 70 students
2. Next, we need to account for the students who are enrolled in exactly two of the classes. According to the given information, there are 24 students who fall into this category.
3. To calculate the total number of students in all three classes, we need to subtract the students enrolled in exactly two classes (24) from the sum of the individual class enrollments. This accounts for the double-counting of the students who are in two classes.
Total students in all three classes = Biology + Chemistry + Physics - Students enrolled in exactly two classes
Total students in all three classes = 50 + 60 + 70 - 24
4. Finally, perform the calculation:
Total students in all three classes = 180 - 24 = 156
Therefore, there are 156 students enrolled in all three classes (Biology, Chemistry, and Physics) at Small Town High.