Question

Suppose 18% of the students at a college receive some academic scholarship, 43% receive some need-based financial aid, and 52% receive academic scholarship or need-based financial aid (or both). What is the percentage receives both?

Answer 1

Answer:

38%

Step-by-step explanation:

Percentage of the students at a who receive academic scholarship(A)=18

Percentage of the students at a who receive need-based financial aid(B)=43

Percentage of the students at a who receive academic scholarship or need-based financial aid (or both). =52

Now from Set Theory,

n(A∪B)= n(A)+n(B)-n(A ∩ B)

Written in Words

n(A OR B) = n(A)+n(B)-n(A AND B)

Total Percentage=100

100 =18+44-n(A AND B)

100=62-n(A AND B)

n(A AND B)=100-62=38

This means percentage who receive BOTH=38%