SOLUTION: Everyone in a class of 30 students takes math and history. Seven students received an A in history, 13 received an A in math, and 4 received an A in both courses. How many students

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Question 257923: Everyone in a class of 30 students takes math and history. Seven students received an A in history, 13 received an A in math, and 4 received an A in both courses. How many students did not receive an A in either course?
Answer by Theo(13342) About Me  (Show Source):
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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.