MATH SETS AND COUNTING
posted by LEILA
There are a total of 103 foreign language students in a high school where they offer only Spanish, French, and German.
You are given the following details for this semester:
44 take Spanish.
44 take French.
42 take German.
7 take Spanish and French but not German.
5 take Spanish and German but not French.
5 take French and German but not Spanish.
22 students are taking at least two languages.
(1) How many students take all three languages in this semester?
(2) How many students take only French in this semester?

Teunis
There are a total of 103 foreign language students in a high school where they offer only Spanish, French, and German.
Call these groups S F G SF SG FG FGS
You are given the following details for this semester:
7 take Spanish and French but not German.
SF = 7
5 take Spanish and German but not French.
SG = 5
5 take French and German but not Spanish.
GF = 5
44 take Spanish.
S + SF + SG + FGS = 44 > S + FGS = 32
44 take French.
F + SF + FG + FGS = 44 > F + FGS = 32
42 take German.
G + SG + FG + FGS = 42 > G + FGS = 32
22 students are taking at least two languages.
SF + SG + GF + FGS = 22 > FGS = 22  7 5 5 = 5
(1) How many students take all three languages in this semester? FGS = 5
(2) How many students take only French in this semester?
F + FGS = 32 > F = 32  5 = 17
Respond to this Question
Similar Questions

math
There are a total of 152 foreign language students in a high school where they offer only Spanish, French, and German. You are given the following details for this semester: 58 take Spanish. 71 take French. 66 take German. 9 take Spanish … 
math
107 total foreign language students 42 take spanish 46 take french 45 take german 8 take spanish & french but not german 6 take french & german but not spanish 8 take spanish & german but not french 24 students are taking at least … 
math
There are a total of 107 foreign language students in a high school where they offer only Spanish, French, and German. 42 take Spanish. 46 take French. 45 take German. 8 take Spanish and French but not German. 8 take Spanish and German … 
Math
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 … 
Math
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 … 
Math  Probabilities
There are a total of 116 foreign language students in a high school where they offer Spanish, French, and German. There are 22 students who take at least 2 languages at once. If there are 47 Spanish students, 45 French students, and … 
Math
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 107 students in the school. There are 42 in the Spanish class, 32 in the French class, and … 
Math
There are a total of 103 foreign language students in a high school where they offer Spanish, French, and German. There are 29 students who take at least 2 languages at once. If there are 40 Spanish students, 42 French students, and … 
math
An elementary school is offering 3 language classes: one in Spanish, one in French, and one in German. These classes are open to any of the 93 students in the school. There are 35 in the Spanish class, 31 in the French class, and 22 … 
maths
In a survey of 100 students, the number s studying various languages were found to be: Spanish, 28; German, 30; French, 42; Spanish and German, 8; Spanish and French, 10; German and French, 5; all three languages, 3. (a)How many students …