A survey of Chaicago sports fans asked them 3 questions about which they prefer. Each fan must give exactly 1 answer to each question. Given a choice between the Cubs and White SOx, 40% chose cubs. Between the Bulls and Blackhawks, 57% chose bulls. between wildcats and maroons, 73% chose wildcats. 18% chose the cubs, wildcats, and bulls. 5% chose white sox, black hawks, and maroons. Of the people who chose cubs, 55% chose bulls. Of the people who chose cubs and wildcats, 60% chose bulls. Of the people who chose White Sox, what percentage chose both bulls and maroons?

Question

A survey of Chaicago sports fans asked them 3 questions about which they prefer. Each fan must give exactly 1 answer to each question. Given a choice between the Cubs and White SOx, 40% chose cubs. Between the Bulls and Blackhawks, 57% chose bulls. between wildcats and maroons, 73% chose wildcats. 18% chose the cubs, wildcats, and bulls. 5% chose white sox, black hawks, and maroons. Of the people who chose cubs, 55% chose bulls. Of the people who chose cubs and wildcats, 60% chose bulls. Of the people who chose White Sox, what percentage chose both bulls and maroons?

PLEASE HELP. I TRIED IT, BUT IT DOESNT SEEM TO WORK. I GOT 25%??? WITH A TON OF VENN DIAGRAMS.....BUT ITS WRONG

Answer 1

To solve this problem, we can use a technique called proportional reasoning. Let's break down the information provided step by step.

1. We know that 40% of the Chicago sports fans chose the Cubs, and 18% of the fans chose the Cubs, Wildcats, and Bulls. This means that 18% of the fans who chose the Cubs also chose the Bulls.

2. We are also given that 57% of the fans chose the Bulls. Since 18% of the Cubs fans chose the Bulls, the remaining 57% - 18% = 39% of the Bulls fans did not choose the Cubs.

3. Now, we need to find the percentage of White Sox fans who chose both Bulls and Maroons. We know that 5% of the fans chose the White Sox, Blackhawks, and Maroons. Let's denote the percentage of White Sox fans who chose both Bulls and Maroons as "x%".

4. We know that 39% of the Bulls fans did not choose the Cubs, so the percentage of Bulls fans who also chose the Maroons is 100% - 39% = 61%.

5. We also know that 5% of the fans who chose the White Sox, Blackhawks, and Maroons. Since all these fans also chose the Blackhawks, we can subtract this overlapping percentage to find the percentage of White Sox fans who chose both Bulls and Maroons, but not the Blackhawks. This gives us x% - 5%.

6. Now, we can create an equation using the data above:
- Percentage of White Sox fans who chose both Bulls and Maroons, but not the Blackhawks (x% - 5%), is equal to 61%.

Therefore, x% - 5% = 61%.

7. Solving the equation, we find:
x% - 5% = 61%
x% = 61% + 5%
x% = 66%

Therefore, the percentage of White Sox fans who chose both Bulls and Maroons is 66%.