Question

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?

Answer 1

This can be solved using formula for Venn Diagrams:

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

Where, the n in front indicates number of items [ n(A) is number of elements in set A ]

We can take:

• set A as students taking Ethics
• set B as students taking Metaphysics

Given:

Tota = 15,000

n(A) = 2200

n(both A and B) = 1700

n(neither A nor B) = 9500

Substituting these into our formula, we get:

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

Hence, 5000 students are taking metaphysics this term.

*** If we want to know students taking metaphysics ONLY, we can subtract n(both A and B) from 5000. So we have
`5000-1700=3300` ***

ANSWER:

Total students taking Metaphysics = 5000

Students taking Metaphysics only = 3300