There are a total of 127 foreign language students in a high school where they offer Spanish, French, and German. There are 19 students who take French and German, 16 students who take French and Spanish, 13 students who take German and Spanish, and 2 students who take all three languages. If there are 57 Spanish students, 58 French students, and 58 German students, find:

Step-by-step explanation:

Even though there is no questiond asked, it is probably about venn diagrams. The Venn diagram of this situation is attached.

At first, we locate all the students that are learning all three languages (2) . Recall that given two languages, the number of students that are in the intersection between the given languages must add to the number from the statement.  Then, we know that 19 students take French and German, so 17 study French and German only (since 2 already take French and German). The same way, we know that 16 students take French and spanish, so 14 take Spanish and French only. Finally, by the same reasoning, we know that 11 students take Spanish and German only.

The numbers of each language should also add to the total said in the statement. Hence for the case of spanish, we have that

x+11+2+14 = 57 (where x is the number of students that take spanish). This implies that x=30.

On the same way, we can figure out that 25 students take only French (25+14+2+17 = 58) and that 28 students take only German (28+2+11+17=58).

Recall that we have a total of 30+14+25+2+11+17+28= 127. So this means that every student take at least one language (there is no student that takes no language classes).

58 - 19-16-2  = 21  students study only french  

58 - 19 - 13 - 2 = 24 students study only german

57 - 16 - 13 - 2 = 26 students study only Spanish

Step-by-step explanation:

The first thing you can do is a drawing to help you understand what is going on, I attach the drawing below.

To find the students that study only french you subtract the students that study french and Spanish and the students that study  german and french and the students that study all three languages

58 - 19-16-2  = 21  students study only french  

similarly

58 - 19 - 13 - 2 = 24 students study only german

57 - 16 - 13 - 2 = 26 students study only Spanish