The wilson family invited 100 relatives to their christmas party. 90 guests had dutch heritage, 80 had german heritage and 75 had english heritage. what is the minimum number of people who claimed ancestry from all three heritages?

To comprehend let’s assume:
100 relatives as 100 tiles
Now, 90 Dutch people fills 90 tiles.
Since we require minimum common people as the question suggests we need to make common tiles less in Number.

80 German people fills 10 empty tiles and 70 Dutch people tile.
Now 10 German tiles, 20 Dutch tiles and 70 common tiles. Again do the same, fill non common tiles first with English. i.e.
10 German + English, 20 Dutch + English. 
So only 45 Dutch + German + English.

Hence 45 is the answer.

for me this my answer o fortunately, they did not notice, and i could pretend not to care.​   i hope this you