Students at the Zoo - Solution and Analysis

(Solution Hidden)


Solution:

75 students ate something. Since there were a total of 90 students who went to the zoo, the answer is that 15 had nothing.

Analysis:

1. To find out how many students had nothing, we first need to figure out how many students had at least one item.

2. First, we add the number who had Popsicles, the number who had hot dogs, and the number who had sodas. This is P+S+H = 38+33+24 = 95

3. Students who had two items were counted twice in the above step. So, we need to subtract off (P+S), (S+H), and (P+H). This means, 95 - 10 - 5 - 8 = 72.

4. Now, this is a little tricky. We need to add back the number of students who had all three. The reason for this is that these students were counted 3 times in step 2, but they were subtracted off 3 times in step 3 (i.e. they are counted in each pair). So, 72 + 3 = 75.

5. Since 75 had at least one item, then 15 students had nothing at the zoo.

Now that we have understood and derived the solution logically, we can state that the solution is a formula from set theory. It is finding the total membership of 3 intersecting sets

Given sets P,Q,R: total membership = P + Q + R - (PnQ) - (PnR) - (QnR) + (PnQnR)
where n represents intersection.