Question

In a stadium 4/9 of the attendees are fans of the home team and 2/11 of the attendees are fans of the visitor's team. If there are 24,000 attendees in total, and none of them likes both teams, how many attendees are not fans of any of the two teams?

a) 6,000
b) 9,000
c) 10,000
d) 15,000

Answer 1

To find the number of non-fan attendees, calculate the number of fans for both teams and subtract from the total attendees. Approximately 10,667 attendees are fans of the home team, 4,364 are fans of the visiting team. The closest option to the number of non-fans is 9,000.

Step-by-step explanation:

To determine how many attendees at the stadium are not fans of either the home or visitor's teams, we need to calculate the number of fans for each team and subtract it from the total attendees. According to the student's question, 4/9 of the attendees are fans of the home team and 2/11 of the attendees are fans of the visitor's team.

First, calculate the home team fans: (4/9) × 24,000 = 10,667 (approx).

Next, calculate the visitor's team fans: (2/11) × 24,000 = 4,364 (approx).

Now, to find the number of attendees who are not fans of either team, subtract the sum of home and visitor's team fans from the total attendees: 24,000 - (10,667 + 4,364) = 24,000 - 15,031 = 8,969 (approx). Therefore, the closest option to the number of non-fans is 9,000.