Holidays

Of the 35 students of class were 7 on holiday in Germany and just as much in Italy. 5 students visited Austria. In none of these countries was 21 students, all three visited by one student . In Italy and Austria were 2 students and in Austria and Germany was 1 student. How many students visited Germany or Italy (a), Austria or Italy (b), Germany or Austria (c)?

Correct result:

a =  14
b =  9
c =  10

Solution:


n+x+1+1 = 7
x+i+1+2 = 7
1+1+2+r = 5
n+x+i+r+1+1+2 = 35-21
a = 7+7-x
b = r+i+x+1+1+2
c = n+x+1+1+2+r

n+x = 5
i+x = 4
r = 1
i+n+r+x = 10
a+x = 14
b-i-r-x = 4
c-n-r-x = 4

a = 14
b = 9
c = 10
i = 4
n = 5
r = 1
x = 0

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