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

Answer 1

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.

Answer 2

Typo... I subtracted 19 to get 103..

Answer 3

Answer

Answer 4

12