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 9 students who have Mr. Green for math and nothing else. Use the Venn diagram below:
A Venn diagram of three overlapping circles titled 'Band,' 'Choir,' and 'Math' is shown.
· The circle on the left titled 'Band' contains the number 11 in the part of the circle that is not overlapping with any other circle.
· The circle on the right titled 'Choir' contains the number 17 in the part of the circle that is not overlapping with any other circle.
· The circle above the other two circles titled 'Math' is empty in the part of the circle that is not overlapping with any other circle.
· The region where all three circles overlap in the middle of the diagram contains the number 3.
· The region where the 'Band' circle overlaps with the 'Math' circle and does not include the intersection of all three circles contains the number 7.
How many students take exactly 2 classes with Mr. Green?
We have the following values from the Venn diagram:
- 11 students take band only
- 17 students take choir only
- 9 students take math only (not included in the diagram)
- 3 students take all three classes
- 7 students take band and math, but not choir
There are 25 students in the band. We know that 11 students take band only, 7 take band and math, and 3 take all three classes. This leaves 25 - 11 - 7 - 3 = 4 students who take band and choir but not math.
Since there are 57 students in total who take at least one class with Mr. Green, there should be 57 - 11 - 17 - 9 - 3 - 7 - 4 = 6 students who take choir and math but not band.
So, the number of students who take exactly 2 classes with Mr. Green is 4 (band and choir) + 7 (band and math) + 6 (choir and math) = 17 students. Answer: \boxed{17}.
To find out how many students take exactly 2 classes with Mr. Green, we need to calculate the sum of the numbers in the intersecting regions of the Venn diagram.
1. The region where the 'Band' circle overlaps with the 'Math' circle and does not include the intersection of all three circles contains the number 7.
2. The region where all three circles overlap in the middle of the diagram contains the number 3.
So, the total number of students who take exactly 2 classes with Mr. Green is 7 + 3 = 10.
To find the number of students who take exactly 2 classes with Mr. Green, we need to look at the overlapping regions of the Venn diagram.
First, let's determine the number of students who take both Band and Choir classes. From the Venn diagram, we see that the overlapping region between Band and Choir is represented by the number 3.
Next, let's determine the number of students who take both Band and Math classes. From the Venn diagram, we see that the overlapping region between Band and Math (excluding the intersection with all three circles) is represented by the number 7.
Now, let's determine the number of students who take both Choir and Math classes. Since there is no number given for this region, we can assume that there are no students who take both Choir and Math classes.
To find the total number of students who take exactly 2 classes, we need to sum up the number of students in each of these overlapping regions: students in Band and Choir (3) + students in Band and Math (7) = 3 + 7 = 10.
Therefore, there are 10 students who take exactly 2 classes with Mr. Green.