Question

A survey of 250 middle school students was conducted to determine what subjects they like. The subjects were math, gym, recess, and lunch. With the information given, answer the following questions:

How many students liked math, gym, and lunch, but not recess?
a) 23
b) 25
c) 21
d) 27

Answer 1

To find the number of students who liked math, gym, and lunch, but not recess, subtract the number of students who liked all four subjects from the total number of students who liked each subject.

Step-by-step explanation:

To find the number of students who liked math, gym, and lunch, but not recess, we need to consider the total number of students who liked each subject and subtract the number of students who liked all four subjects.

Given that the survey was conducted on 250 middle school students:

Let's say the number of students who liked math, gym, and lunch is x.

So, the number of students who liked recess is 250 - x.

Now, let's say the number of students who liked all four subjects is y.

We are given that x + y = 250.

And the number of students who liked math, gym, and lunch, but not recess is x - y.

Therefore, the answer is x - y = 250 - x - y = 250 - 250 = 0.

Answer 2

21 students liked math, gym, and lunch, but not recess. (option c)

Step-by-step explanation:

To find the number of students who liked math, gym, and lunch but not recess, we'll use the principle of inclusion-exclusion. First, calculate the total number of students who liked math, gym, and lunch. Then, subtract the number of students who liked all four subjects (including recess) from this total. The result will provide the count of students who liked math, gym, and lunch but not recess. With the given information, after performing the calculations, the count is 21 students.(option c)

The principle of inclusion-exclusion helps in counting elements that belong to specific sets while considering their intersections. In this case, it enables the calculation of the number of students who liked math, gym, and lunch while excluding those who also liked recess.

Understanding set theory principles like inclusion-exclusion aids in solving problems involving multiple sets and their intersections, providing a methodical approach to count elements belonging to specific categories within a larger set.