Find the number of pure bloods

Question

In a far-away land called Encantadia, 200 citizens are gathered to attend the wed- ding of Queen Mine-a and Prince Ybrahim. These citizens come from the three main kingdoms of Encantadia: Lireo, Sapiro, and Hathoria. The citizens can be pure blood (pure Lirean, pure Sapirean, or pure Hathor), or might have mixed lineage; i.e., a Lirean might have a Sapirean parent and a Hathor parent, and so on. Among the 200 citizens, 20 have Lirean-Sapirean lineage, but no Hathor ancestry, and 60 Hathors are mixed blood. If exactly 100 Lireans, 100 Sapireans, and 100 Hathors are present at the event, find the number of pure bloods.

Answer 1

I found a Venn diagram helpful in answering this question.

 

The way I read the problem, you could have three circles that intersect two at a time or all three at once in the center. Picture a red, a blue, and a yellow circle overlapping. They would make a purple part where red and blue overlap, a green for the blue and yellow, an orange for the red and yellow, and a brown spot in the middle where all three circles touch.

 

Let the red circle represent Lirean lineage, the blue represent Sapirean, and the yellow be Hathorean. There are 20 Lirean-Sapirean-no-Hathor, so 20 in the purple. 60 people have some amount of Hathorean lineage, so the orange, brown, and green combined have 60 people in them.

 

That covers all of the mixed blood areas. A total of 80 people have mixed blood. Since there are only 200 people at the event, 120 must be pure blood. The information about there being 100 of each type is superfluous, but you may use it to run possible numbers and check.