There are 12 people on the basketball team and 33 people on the football team. If 110 people attend the athletic banquet...

a) what is the maximum and minimum of people that are on both the basketball and football teams?

b) what is the maximum and minimum of people that are on neither of these teams

Venn diagram is helpful

Explanation below, let me know if it does not fully make sense to you.  

Step-by-step explanation:

Venn Diagram is very helpful.  

So, the simple way of describing is that all members of the smaller team could be in the larger team, so this would be the maximum  number of people that could be on both.  The minimum is 0, so none are on both.  This works because since the total number of people that attend the banquet is larger than 12+33 this means there can be extra.  if the number of people that attended the banquet was even 44, this would mean at least one person would need to be on both.

For the max and min of not on either, we look at the two cases in the first part.  So if everyone on the baset ball team is also on the football team, there would be 110-33 people left, since the 33 on the football team also include the 12 on the basketball team, so you'd only have to count the 33.

If there is no intersect, then you have to subtract both groups, so 110 - 12 - 33.  If this doesn't fully make sense let me know and I can try explaining more thoroughly.