You must Love Baseball!

Today I will be solving this problem of the week. It is called, You must love Baseball!

Solution
The problem states that at least one fan from each group was absent. This means that, since there are 30 kids, the maximum number of students is 28. Also the maximum number of fans would be 21-1=20, and the maximum number of non-fans would be 9-1=8. 

Over half the class was present so there was at least 16 students. Since 3/4 of the class that was here were baseball fans, the fraction of non-fans is 1/4. 

What we need to do to find the answer to the problem, is look for all the numbers from 16 to 28 that is divisible by 4. Those numbers are 16,20,24, and 28. any one of those, or possibly all of them could fit the bill for this problem. I am going to solve all of them individually.

16
Number absent: 30-16=14
Number of fans: 3/4 *16=12
Number of non-fans:1/4*16=4

This solution is valid because it fulfills all of the items on the checklist displayed in the problem. 16 is a possible solution to this problem.

20
Number absent: 30-20=10
Number of fans: 3/4*20=15
Number of non-fans: 1/4*20=5

This is also a valid solution because it also follows the checklist displayed in the problem. 20 is a possible solution.


24
Number absent: 30-24=6
Number of fans: 3/4*24=18
Number of non-fans: 1/4*24=6

This is also a valid solution to the problem because it also follow the checklist displayed in the problem. 24 is a possible solution. 

28
Number absent: 30-28=2
Number of fans:3/4*28=21
Number of non-fans:3/4*28=7

This is not a possible solution to the problem because, in the checklist it states that at least one person is absent from each group, but if 28 students were here and 3/4 of them were fans, there would be 21 fans, which means that no fan was absent, which makes 28, not a solution.

Conclusion
In conclusion, there is not enough information given in the problem to determine only one possible solution, that follows the following criteria: at least one fan and non-fan is absent, more than half the class was present and the probability of asking a baseball fan a question was 3/4. My conclusion is validated by the fact there are 3 possible solution to this problem. In order for their to have to be enough information, only one possible solution was supposed to arise. One piece of information Mr.Fann could have provided to eliminate 2 of the 3 solutions, is,"there was less than 15 fans present. This would eliminate 20 and 24, leaving 16 as the only possible solution. Post your own solution and one thing Mr.Fann could have added to eliminate 2 of the 3 solutions. in the comments section down below.