There are 75 students in the Travel Club. They discovered that 27 members have visited Mexico 34 have visited Canada, 12 have been to England, 18 have visited both Mexico and Canada, been only to England, and 8 have been only to Mexico. Some club members have not been te of the three foreign countries and, curiously, and equal number have been to all three countries a) How many students have been to all three countries? b) How many students have been only to Canada?
Answers
Answer:
Step-by-step explanation:
Total students = 75
Visited Mexico = 27 = M
Visited Canada = 34 = C
Visited England = 12 = E
Visited Mexico & Canada = 18 = M∩C
Only to England = 6 = E only
Only to Mexico = 8 = M only
Visited no country = X
Visited all country = X M∩C∩E
Total Students = M + C + E - M∩C - M∩E - E∩C + M∩C∩E + No country
=> 75 = 27 + 34 + 12 - 18 - M∩E - E∩C + X + X
=> M∩E + E∩C = 2X - 20
Only Mexico = M - M∩E - M∩C + M∩C∩E
=> 8 = 27 - M∩E - 18 + X
=> M∩E = X + 1
Only England = E - M∩E - E∩C + M∩C∩E
=> 6 = 12 - X -1 - E∩C + X
=>E∩C = 5
Only Canada = C - M∩C - E∩C + M∩C∩E
=> Only Canada = 34 - 18 - 5 + X
=> Only Canada = 11 + X
M∩E + E∩C = 2X - 20
=> M∩E + 5 = 2X - 20
=> M∩E = 2X - 25
M∩E = X + 1
=> 2X - 25 = X + 1
=> X = 26
its not possible that 26 people visited all countries
So some data is wrong
With Some different Data Solved
With changed data
Total students = 40
Visited Mexico = 17 = M
Visited Canada = 28 = C
Visited England = 10 = E
Visited Mexico & Canada = 12 = M∩C
Only to England = 3 = E only
Only to Mexico = 4 = M only
Visited no country = X
Visited all country = X M∩C∩E
Total Students = M + C + E - M∩C - M∩E - E∩C + M∩C∩E + No country
=> 40 = 17 + 28 + 10 - 12 - M∩E - E∩C + X + X
=> M∩E + E∩C = 2X + 3
Only Mexico = M - M∩E - M∩C + M∩C∩E
=> 4 = 17 - M∩E - 12 + X
=> M∩E = X + 1
Only England = E - M∩E - E∩C + M∩C∩E
=> 3 = 10 - X -1 - E∩C + X
=>E∩C = 6
M∩E + E∩C = 2X + 3
=> M∩E + 6 = 2X +3
=> M∩E = 2X - 3
M∩E = X + 1
=> 2X - 3 = X + 1
=> X = 4
Only Canada = C - M∩C - E∩C + M∩C∩E
=> Only Canada = 34 - 18 - 5 + 4
=> Only Canada = 15
Answer:
Total students = 75
Visited Mexico 27 = M =
Visited Canada = 34 = C
Visited England = 12= E
Visited Mexico & Canada = 18 = MNC
Only to England = 6 = E only
Only to Mexico = 8 = M only
Visited no country = X
Visited all country = X MOCNE
Total Students = M + C+E MOC- MOE- -
ENC + MnCNE + No country
=>75=27+34 +12-18 MNE - ENC+X+X
=>MOE+ EnC=2x-20
Only Mexico M-MOE MNC + MOCNE
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