In a school, there are 190 students. The number of students who like Pepsi is 100 and is the same as the number of students who like Cola which is same as the number of students who like Fanta. The number of students who like exactly one of the three drinks is 110. If each student likes at least one drink, find the number of students who like all the three drinks.253020Cannot be determined
Question
In a school, there are 190 students. The number of students who like Pepsi is 100 and is the same as the number of students who like Cola which is same as the number of students who like Fanta. The number of students who like exactly one of the three drinks is 110. If each student likes at least one drink, find the number of students who like all the three drinks.253020Cannot be determined
Solution
The problem states that there are 190 students in total. It also states that the number of students who like each drink (Pepsi, Cola, and Fanta) is 100. This means that there are 300 total "likes" distributed among the students.
The problem also states that 110 students like exactly one drink. This means that there are 190 total "likes" left to be distributed among the students who like more than one drink.
Since each student likes at least one drink, the remaining 80 students must like either two or three drinks.
The problem asks for the number of students who like all three drinks. Let's denote this number as x.
Since each of these x students likes all three drinks, they contribute a total of 3x "likes" to the pool of 190 "likes" that are left.
The remaining (80 - x) students must therefore contribute (190 - 3x) "likes". Since each of these students likes exactly two drinks, we can write the equation:
2 * (80 - x) = 190 - 3x
Solving this equation for x gives:
x = 30
Therefore, there are 30 students who like all three drinks.
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