According to a survey made among 200 students, 140 students like cold drinks, 120 students like milkshakes, and 80 like both. How many students like at least one of the drinks?
Understand the Problem
The image contains a word problem. We are given the number of students who like cold drinks, the number of students who like milkshakes, and the number of students who like both. We need to find the number of students who like at least one of the drinks.
Answer
180
Answer for screen readers
180
Steps to Solve
- Identify the given information
Number of students who like cold drinks = 140 Number of students who like milkshakes = 120 Number of students who like both = 80 Total number of students surveyed = 200
- Use the principle of inclusion-exclusion
To find the number of students who like at least one of the drinks, we can use the inclusion-exclusion principle:
$|A \cup B| = |A| + |B| - |A \cap B|$
Where:
$|A \cup B|$ is the number of students who like at least one drink $|A|$ is the number of students who like cold drinks $|B|$ is the number of students who like milkshakes $|A \cap B|$ is the number of students who like both
- Plug in the values
$|A \cup B| = 140 + 120 - 80$
- Calculate the result
$|A \cup B| = 260 - 80 = 180$
So, 180 students like at least one of the drinks.
180
More Information
The principle of inclusion-exclusion is useful in counting problems to avoid double-counting elements that belong to multiple sets. In this problem, we needed to subtract the number of students who like both drinks to avoid counting them twice.
Tips
A common mistake is simply adding the number of students who like cold drinks and the number of students who like milkshakes, without subtracting those who like both. This would lead to double-counting the students who like both, resulting in an incorrect answer.
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