Praxis Core Math- Word Problem

Question

In a class of 78 students, 41 are taking French and 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?

 

The answer is 24, but I have worked the problem 2 different ways and I am not coming up with that answer. What am I doing wrong?

 

Method 1 (incorrect)

41 French - 9 taking both = 32

22 German - 9 taking both = 13

 

add total number of only French and only German, then subtract from total number of students

 

32+13=45, then subtract from total

78-45=33 (this answer is not correct, but why?)

 

Method 2 (incorrect)

add total number of French and German, then subtract students tasking both

 

41+22=63

 

63-9= 54 (this answer is also incorrect, but how do I get to the correct one?)

 

Answer 1

Method 1 works, but you are forgetting about the 9 cross-over students. If you subtract them from the 33, you are left with 24. A Venn Diagram would make this easier to follow.