A certain college has 86 students each of whom has to study at least two of the three courses offered.64 students are studying Meteorology,51philosophy,and 62 sociology.
a)how many students study all the three subject?
b)how many are studying Meteorology and Philosophy only?
c)how many are studying Sociology and Philosophy only?
The equations I get (and I'll let you work it out where the symbols were in the Venn diagram I drew) are:
a + b + x = 64 .... (1)
a + c + x = 51 .... (2)
b + c + x = 62 .... (3)
a + b + c + x = 86 .... (4)
Solve these four equations simultaneously for a, b, c and x.
Big hint: x = 5.