Question
A group of 368 students were surveyed about the courses they were taking at their college
with the following results:
145 students said they were taking Math.
223 students said they were taking English.
225 students said they were taking History.
92 students said they were taking Math and English.
98 students said they were taking Math and History.
159 students said they were taking English and History.
80 students said they were taking all three courses.
How many students took English and History, but not Math?
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with the following results:
145 students said they were taking Math.
223 students said they were taking English.
225 students said they were taking History.
92 students said they were taking Math and English.
98 students said they were taking Math and History.
159 students said they were taking English and History.
80 students said they were taking all three courses.
How many students took English and History, but not Math?
Question Help: QMessage instructor
Ask by Harmon Thornton. in the United States
Mar 22,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
79 students took English and History, but not Math.
Solution
Let
and that
where
We want to find the number of students taking English and History but not Math, which can be written as
This is calculated by subtracting the number of students taking all three courses from the students taking both English and History:
Substitute the given numbers:
Thus,
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
To find the number of students who took English and History but not Math, we can use the principle of inclusion-exclusion. First, we know that 159 students are taking English and History, and among them, 80 are also taking Math. Therefore, we can subtract those taking all three from the total English and History:
159 (English and History) - 80 (all three) = 79 students.
So, there are 79 students who took English and History, but not Math!
Now, if you’re trying to solve similar problems, remember to clearly define your overlapping sets! It’s easy to miss an intersection or double count if you don’t sketch a Venn diagram. Start with small groups to visualize relationships before moving to larger datasets.
