Expert: Steve Holleran - 12/9/2007

Question
Studying for the CLEP, and haven't taken/used math in years. I  remembered enough for many of these kinds of problems, but this one asks "how many don't." See for yourself:

"There are 50 students in a class. Of these, 30 like vanilla ice creme and 25 like chocolate. Of that group, 10 like both vanilla and chocolate. How many students don't like vanilla or chocolate?"

I represented it like 30v+25c=50; v+c=10. I was able to get v and c out of that. I can't figure out how to represent the "neither one" concept algebraically. I also don't see any "not" problems like this on any algebra web site. Would appreciate the help. Thanks.

Answer
Hi Nicholas,

Actually, the best device to use to solve these is a Venn diagram.  If you are not familiar with them , basically you have two circles which overlap a little bit, like the Mastercard symbol.  If you call one circle Vanilla and the other Chocolate, then the overlapping region is the 10 students who like both.  Then if 30 like vanilla, put 20 in the vanilla circle, but outside of the overlapping region.

For the 25 that like chocolate, put 15 in the chocolate circle, but outside of the overlapping region.  (Of the 25, 10 were already counted.

Now if you add the regions up, you have 20 + 10 + 15 = 45, so the other 5 don't like vanilla or chocolate.

This is really easy to do visually, but I don't know how to show it here.

Hope I helped a little.
STeve