To find the number of students who take exactly 2 classes, we need to add up the numbers in the overlapping regions of the Venn diagram.
- The region where the 'Band' and 'Math' circles overlap but do not include the intersection of all three circles contains 7 students.
- The region where the 'Choir' and 'Math' circles overlap but do not include the intersection of all three circles is empty (since the 'Math' circle is empty in that region).
- The region where the 'Band' and 'Choir' circles overlap but do not include the intersection of all three circles contains x students (which we want to find).
We can use the formula:
total = band + choir + math - (band and choir) - (band and math) - (choir and math) + (band and choir and math)
Plugging in the values we know:
57 = 25 + 17 + 0 - x - 7 - 0 + 3
Simplifying:
57 = 38 - x
x = 38 - 57
x = 19
Therefore, there are 19 students who take exactly 2 classes with Mr. Green.
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?
1 answer
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