# 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?

1
by mygimail

2015-11-25T12:35:48+08:00
Let x be the number of humans.
y be the number of horses.

Since there are 74 heads, we can form the equation:
x + y = 74

And since there are 196 legs, and we all know that a human has 2 legs and a horse has 4 legs, we can form the equation:
2x + 4y = 196

So, we can now solve for the value of x and y using the two equations.
x + y = 74
2x + 4y = 196

x + y = 74 can be transformed as y = 74 - x. We can substitute this to the value of y in the other equation. Therefore, we have:
2x + 4y = 196
2x + 4(74-x) = 196
2x + 296 - 4x = 196
2x - 4x = 196 - 296
-2x = -100
x = -100/-2
x = 50

From the value of x, we can get the value of y.
x + y = 74
(50) + y = 74
y = 74 - 50
y = 24

Therefore, there are 50 humans and 24 horses.

- D.E.