Here are 15,000 students at college x. of those students, 1,700 are taking both ethics and metaphysics this semester. there are

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1 month ago

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Here are 15,000 students at college x. of those students, 1,700 are taking both ethics and metaphysics this semester. there are

2,200 total students taking ethics. 9,500 students are taking neither of these classes. how many students are taking metaphysics this term?

Mathematics

2 answers:

zzz [12.3K] · Answer 1 · 2026-03-31T12:02:58+03:00

zzz [12.3K]1 month ago

7 0

I believe there are 1,600 students enrolled in metaphysics.

Inessa [12.5K] · Answer 2 · 2026-03-31T12:03:19+03:00

The problem can be approached using the formula for Venn Diagrams:

Total = n(A) + n(B) - n(both A and B) + n(neither A nor B)

Here, the n signifies quantity [ n(A) represents the number of elements in set A ]

We can define:

set A as students taking Ethics
and set B as those enrolled in Metaphysics

Provided information:

Total = 15,000

n(A) = 2200

n(both A and B) = 1700

n(neither A nor B) = 9500

Plugging this data into our formula yields:

$15,000=2200+n(B)-1700+9500\\15,000=n(B)+10,000\\n(B)=15,000-10,000\\n(B)=5000$

Therefore, 5000 students are taking metaphysics this semester.

*** If we wish to find out how many are taking only metaphysics , we can deduct n(both A and B) from 5000. Thus, we conclude *** $5000-1700=3300$ ***

ANSWER:

Total students enrolled in Metaphysics = 5000

Students taking only Metaphysics = 3300