An investigator interviewed 100 students to determine the performance of three drinks: milk, coffee and tea. The investigator reported that 10 students take all three drinks milk, coffee and tea; 20 students take milk and coffee; 25 students take milk and tea; 20 students take coffee and tea; 12 students take milk only; 5 students take coffee only and 8 student take tea only. Then the number of students who did not take any of three drinks is 10 20 25 30
Question
An investigator interviewed 100 students to determine the performance of three drinks: milk, coffee and tea. The investigator reported that 10 students take all three drinks milk, coffee and tea; 20 students take milk and coffee; 25 students take milk and tea; 20 students take coffee and tea; 12 students take milk only; 5 students take coffee only and 8 student take tea only. Then the number of students who did not take any of three drinks is 10 20 25 30
Solution
To find the number of students who did not take any of the three drinks, we first need to find the total number of students who did take at least one drink.
Here's how we can do that:
- 10 students take all three drinks (milk, coffee, and tea).
- 20 students take milk and coffee. However, we've already counted the students who take all three drinks, so we subtract those 10 students to avoid double-counting. This leaves us with 20 - 10 = 10 students who take only milk and coffee.
- 25 students take milk and tea. Again, we subtract the 10 students who take all three drinks to avoid double-counting. This leaves us with 25 - 10 = 15 students who take only milk and tea.
- 20 students take coffee and tea. Subtracting the 10 students who take all three drinks leaves us with 20 - 10 = 10 students who take only coffee and tea.
- 12 students take only milk.
- 5 students take only coffee.
- 8 students take only tea.
Adding all these numbers together, we get:
10 (all three) + 10 (only milk and coffee) + 15 (only milk and tea) + 10 (only coffee and tea) + 12 (only milk) + 5 (only coffee) + 8 (only tea) = 70 students.
Since we know that there were 100 students in total, the number of students who did not take any of the three drinks is 100 - 70 = 30 students.
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