Question

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:

How many students take exactly 2 classes with Mr. Green?
i need help with this

Answer 1

band alone 11
choir alone 17

band and choir alone 4
band and math alone 7
math and choir alone 6

band choir and math 3

math alone 9 from 11+4+10+6+17 + M = 57
so
2 classes = 4+7+6 = 17

17 students take exactly two classes with Mr. Green

Answer 2

Explanation:

Given that Mr. Green teaches band, choir and math.

Total students = 57

Students who learn band A = 25

Students who learn math alone =9

From venn diagram we see that

band alone 11

choir alone 17

band and choir alone 4

band and math alone 7

math and choir alone 6

band choir and math 3

math alone 9 from 11+4+10+6+17 + M = 57

so

2 classes = 4+7+6 = 17

17 students take exactly two classes with Mr. Green