Question

In a recent survey of a fraternity, it was discovered that 40% of the men are athletes, 25% are in the Honors Program, and 15% are both athletes and in the Honors Program. Additionally, it was found that only six men are neither athletes nor in the Honors Program. How many members were in the fraternity?

A. 20 members
B. 60 members
C. 80 members
D. 100 members

Answer 1

To find the number of members in the fraternity, we use the principle of inclusion-exclusion and find that the number is approximately 179.

Step-by-step explanation:

To find the number of members in the fraternity, we need to use the principle of inclusion-exclusion. Let's define the following variables:

• A = number of athletes
• H = number of students in the Honors Program
• C = number of students who are both athletes and in the Honors Program
• x = number of students who are neither athletes nor in the Honors Program
• n(A) = percentage of athletes = 40%
• n(H) = percentage of students in the Honors Program = 25%
• n(C) = percentage of students who are both athletes and in the Honors Program = 15%
• n(x) = percentage of students who are neither athletes nor in the Honors Program = 6%

We can use the formula:

n(A∪ H) = n(A) + n(H) - n(C)

n(A∪ H) = 0.40 + 0.25 - 0.15 = 0.50

We know that n(x) = 6%, so we can write the equation:

n(A∪ H) + n(x) = 1

0.50 + 0.06 = 0.56

Therefore, the number of students who are either athletes or in the Honors Program is 0.56. We can find the number of students in the fraternity by dividing this percentage by 100 and multiplying it by the total number of students:

0.56 * N = 100 -> N = 100/0.56 = 178.57

Rounding up to the nearest whole number, we get the approximate number of members in the fraternity as 179. Therefore, the correct answer is D. 100 members.