A new restaurant has opened. They have 100 items to chose from! Of those items…

Question

I need some help with this problem.
A new restaurant has opened. They have 100 items to chose from! Of those items… 45 are fattening 45 are gross 44 are ice-cold 10 are both fattening and gross 18 are both fattening and ice-cold 13 are both gross and ice-cold 3 are gross, ice-cold, and fattening

How many items do they have that are not fattening, not gross, and not ice-cold?

I think to start with 100 - 3 - 13 - 18 - 10 then add on the overlaps maybe. Not sure if this is right or really how to attack this problem.

Answer 1

Let's look at it this way. We know the total is 100 and there are three basic groups described.

We first need to count up how many items are in each group i.e. the 45 fattening, the 45 gross, and the 44 ice-cold.

So:

45 + 45 + 44 = 134

We over counted so now we have to subtract how many items are shared by two of the groups i.e. 10 are both fattening and gross, 18 are both fattening and ice-cold, and 13 are both gross and ice-cold

So:

134 - 10 - 18 - 13 = 93

We now have under counted and have to add the items that fit into each group i.e. 3 are gross, ice-cold, and fattening

So:

93 + 3 = 96

Now we know how many items there are (100) and we know how many can be described by the 3 groups. So the difference is the number of items not in the group.

100 - 96 = 4

So 4 are not fattening, not gross, and not ice-cold.