A survey of a group of 103 people about their eating habits found the following:
60 of the people like sardines,
44 like krill,
17 like pizza and krill,
20 like pizza and sardines,
23 like sardines and krill,
7 like pizza, krill, and sardines,
16 like none of these three things.
I think I have my venn diagram set up correctly, but how do I find out how many people like pizza, but not krill or sardines?
Work out from the middle. You have $7$ who like all three. You have a total of $17$ who like pizza and krill, but $7$ of those also like sardines, so there are $17-7=10$ who like pizza and krill but not sardines. Similarly, there are $13$ who like pizza and sardines only, and $16$ who like krill and sardines only.
That accounts for $7+10+16=33$ who like krill and at least one of the other two foods, and there are $44$ altogether who like krill, so there must be $44-33=11$ who like just krill. Similarly, there are $60-(7+13+16)=24$ who like just sardines.
Those groups account for $7+13+16+11+24=71$ people, and there are another $16$ who like none of the three foods, for a total of $87$ people amongst the categories other than likes only sardines. That leaves $103-87=16$ people for the missing category.
Note that your final statement doesn’t make sense: how can the $16$ people who like none of the three foods like only pizza? They don’t like pizza. (They also don’t like krill and don’t like sardines.)
