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If 100 people were at a party 90 spoke Spanish 80 spoke Italian and 75 spoke Mandarin At least how many spoke all three languages?
Wiki User
∙ 14y ago
45
Check my logic. Draw the Venn diagram. Mark the seven areas S, I, M for those languages only (monoglots); a,b,c for single overlaps (bilingual); T in the middle for trilingual.
Tminimum (words "at least") happens at abcmaximum and that happens at SIMminimum , the limit of which is 0 (zero monoglots, all partgoers bilingual).
From the diagram,
abcT = 100, that is
(1) 2abc + 2T = 200
Also, from the given
(2) abT=80
(3) bcT=75
(4) acT=90
Adding (2...4) we get
(5) 2abc + 3T = 245
Subtracting (1) we get Tmin = 45
Wiki User
∙ 14y ago
Riley Abair
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