Mr. Green teaches band, choir, and math. This year, he has 57 students that take at least one of his classes. He teaches band to 25 students. There are 48 students who take either band or choir or both. There are 9 students who take both math and choir with Mr. Green. Use the Venn diagram below:
How many students take exactly 2 classes from Mr.Green?
Here's a quick rundown of how to fill in the Venn diagram.
1. The 57 students that take at least one of his classes include all students in the three circles (band, choir, and math).
2. We know that 25 students are in the band circle.
3. There are 48 students who take either band or choir or both, meaning that 48-25 = 23 students are in only the choir circle.
4. There are 9 students who take both math and choir, so we add them to both circles in the Venn diagram.
5. To find the total number of students in the choirs and math circles, we add the numbers from steps 3 and 4, which gives us 23+9=32.
6. Since there are 57 students who take at least one class of the three, we can find the number of students in only the math circle by subtracting the total numbers found from steps 2 and 5 from 57, which gives us 57-25-32=0.
7. Now, we know the numbers of students in each circle (25 in band, 23 in only choir, and 0 in only math. 9 in both choir and math).
8. The number of students who take exactly two classes from Mr. Green is the sum of students taking both choir and math, which is 9.
So, there are 9 students who take exactly two classes from Mr. Green.