Question 257923
30 students total.
7 received an a in history.
13 received an a in math.
4 received an a in both courses.
how many students did not receive an a in either course.


20 total received an a in history or math.


of these, 4 received an a in history and math.


those 4 are being counted twice.


once in history and once in math.


you need to subtract 4 from the number who got an a in history or an a in math to get a total of 16 students who got an a in history or in math.


this leaves 30 - 16 = 14 students who did not get an a in either course.


here's the breakdown.


14 students did not get an a in either course.
3 students got an a in history only.
9 students got an a in math only.
4 students got an a in both history and math.

total is 30 students.