Question

There are a total of 134 foreign language students in a high school where they offer Spanish, French, and German. There are

20 students who take French and German,
22 students who take French and Spanish,
12 students who take German and Spanish, and
3 students who take all three languages.

If there are 60 Spanish students, 65 French students, and 60 German students, find:

a) How many students take French only.

b) How many students take French AND German but not Spanish.

c) How many students take French OR German but not Spanish.

Answer 1

Answer: a) 26 students b) 17 students c) 74 students step-by-step explanation: We can make a Venn diagram and make sense of a lot of things a) The number of students who takes French but not German = the number of students who takes French - the number of students who takes French and German = 65 - 20 = 45 students The number of students who takes French Only = The number of students who takes French but not German - the number of students who take French and Spanish + the number of students who take all 3 languages = 45 - 22 + 3 = 26 students.b) The number of students who take French AND German but not Spanish = the number of students who takes French and German - the number of students who take all 3 languages = 20 - 3 = 17 students c) The number of students who take French OR German but not Spanish = the number of students who take French Only + the number of students who take German - the number of students who take German and Spanish = 26 + 60 - 12 = 74 students.

Answer 2

a) 26 students

b) 17 students

c) 74 students

Explanation:

We can make a Venn diagram and make sense a lot of things

a) The number of students who takes French but not German = the number of students who takes French - the number of students who takes French and German = 65 - 20 = 45 students

The number of students who takes French Only = The number of students who takes French but not German - the number of students who take French and Spanish + the number of students who take all 3 languages = 45 - 22 + 3 = 26 students.

b) The number of students who take French AND German but not Spanish = the number of students who takes French and German - the number of students who take all 3 languages = 20 - 3 = 17 students

c) The number of students who take French OR German but not Spanish = the number of students who take French Only + the number of students who take German - the number of students who take German and Spanish = 26 + 60 - 12 = 74 students.