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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?
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
What else can I help you with?
If 100 people were at a party90 spoke Spanish80 spoke Italianand 75 spoke Mandarin. At least how many spoke all three languages?
The minimum number of people who spoke all three languages is 45. This can be calculated by adding the number of people speaking Spanish, Italian, and Mandarin and then subtracting the total number of people at the party. So, 100 - (90 + 80 + 75) = 45.
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