Number of Students

[nycmathguy]

In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?

I know there is a way to solve this using vent diagrams but I forgot. I will guess my way through this problem.

Total number of students in a class = 78.

41 take French
22 take German
9 take both

41 + 22 + 9 = 72

Total number of students in the class minus 72 = 78 - 72 or 6. I say 6 students are not enrolled in either course.

You say?

 

[MathLover1]

so in our task we have equation:
Total = F +G -both +neither
78=41+22-9+neither;
therefore neither=24

 

[nycmathguy]

so in our task we have equation:
Total = F +G -both +neither
78=41+22-9+neither;
therefore neither=24

Cool. This is my main concern, my main struggle in mathematics.