18. 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: a. how many students take exactly 3 classes from mr. green? how many students take exactly 2 classes from mr. green? how many students take exactly 1 class from mr. green?

First, lets gather the information given in the problem :

Mr. G's total students = 57
Mr. G's band students = 25

Clue 1 : Since there are 25 students that take band, that means that there are 57-25 = 32 students who do not take band = 32 students who take choir or math or both.

Mr. G's band / choir / band and choir students = 48

Clue 2 : Since there are 25 students that take band and there are 48 that take either band / choir/ or both, that means we have 48-25 = 23 students who do not take band = 23 students who must take choir but not band. Thus

Mr. G's choir students = 23

So, we have the following :

Mr. G's total students = 57
Mr. G's band students = 25
Mr. G's choir students = 23

However, 25 + 23 = 48. Thus, we have 9 students not accounted for. These must be his math students. Hence,

Mr. G's total students = 57
Mr. G's band students = 25
Mr. G's choir students = 23
Mr. G's math students = 9

Next, they tell us that 9 students take both math and choir.

Without the vin diagrams, this is all I can provide.