Question

One day, a person went to horse racing area, Instead of counting the number of human and horses, he instead counted 74 heads and 196 legs. Yet he knew the number of humans and horses there. How did he do it, and how many humans and horses are there?

Answer 1

@Luis, those two numbers don't even add up to the 74 heads that he sees...

The way you solve this is by a system of equations. If there are x horses and y humans, then the number of heads is \[x+y=74\] and the number of legs (since normally you wouldn't count your own) is \[4x+2y=196\] Solving this simple system gives x=24 and y=50. Thus, there are 24 horses and 50 humans at the race.

Answer 2

Heads are definitively not ignored. So you're saying that there are 33 humans at the race, 33 horses, and yet there are 74 heads? Your solution doesn't use logic, it uses some mistaken assumption that you are free to ignore the actual total number of humans and horses. The correct answer is 24 horses and 50 humans.