TITLE: If there are $74$ heads and $196$ legs, how many horses and humans are there?
QUESTION [39 upvotes]: I was going through some problems then I arrived at this question which I couldn't solve. Does anyone know the answer to this question?

One day, a person went to a horse racing area. Instead of counting the number of humans and horses, he counted $74$ heads and $196$ legs. How many humans and horses were there?

REPLY [42 votes]: Just in case you don't like algebra and don't think in terms of centaurs, here's yet another approach (very close to the centaur version but omitting the mythology).  Suppose for a moment that all 74 heads belong to humans.  Then there would be $2\times 74=148$ legs. That's 48 legs short of the specified number 196.  To get that many extra legs, we have to replace some of the humans with horses. Every time we replace a human with a horse, we gain two legs, so we should do $\frac{48}2=24$ such replacements.  We started with 74 humans, and we need to replace 24 of them with horses, so at the end we have 24 horses and $74-24=50$ humans.