Posted by LEILA on Monday, October 4, 2010 at 10:57am.
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
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