There are a total of 103 foreign language students in a high school where they offer Spanish, French, and German. There are 19 students who take at least 2 languages at once. If there are 38 Spanish students, 38 French students, and 46 German students, how many students take all three languages at once
I played with a Venn Diagram for this one.
I added up 38+ 38+46 and subtracted 103
That leads me to believe that no one took all three languages.
Typo... I subtracted 19 to get 103..
Answer
12
To find the number of students who take all three languages at once, we need to subtract the students who take exactly two languages from the total number of students.
The total number of students is 103.
The number of students who take at least two languages is 19.
We can subtract the number of students who take at least two languages from the total number of students to find the number of students who take only one language:
103 - 19 = 84
Now, let's find the number of students who take all three languages. We know:
- There are 38 Spanish students
- There are 38 French students
- There are 46 German students
To find the number of students who take exactly one language, we can subtract the number of students who take only one language from the total number of students:
84 - 38 (Spanish students) - 38 (French students) - 46 (German students) = 84 - 38 - 38 - 46 = 84 - 122 = -38
Since we obtained a negative number, it means that there is an error in the given information or calculation. Please double-check the numbers provided in the question.