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?

human+horses=74 assuming no two headed

human*2+horses*4=196

solve.

Is it 24 horses and 50 humans.

To solve this problem, let's assume that there were x humans and y horses at the horse racing area.

Now, let's consider the given information. We know that there were a total of 74 heads and 196 legs. Since each person has one head and two legs, and each horse has one head and four legs, we can form two equations based on the number of heads and legs:

Equation 1: x + y = 74 (since the total number of heads is 74)
Equation 2: 2x + 4y = 196 (since the total number of legs is 196)

We can simplify Equation 2 by dividing it by 2:
x + 2y = 98

Now, we have a system of equations that we can solve simultaneously. Here are two different ways to solve it:

Method 1: Substitution
From Equation 1, we can express x in terms of y: x = 74 - y.
Substituting this value of x into Equation 2:
74 - y + 2y = 98
74 + y = 98
y = 98 - 74
y = 24

Substituting the value of y back into Equation 1:
x = 74 - 24
x = 50

Therefore, there were 50 humans and 24 horses at the horse racing area.

Method 2: Elimination
Multiply Equation 1 by 2 to match the coefficients of y:
2x + 2y = 148

Subtract Equation 2 from the multiplied Equation 1:
(2x + 2y) - (2x + 4y) = 148 - 196
2x + 2y - 2x - 4y = -48
-2y = -48
y = (-48) / (-2)
y = 24

Substituting the value of y back into Equation 1:
x + 24 = 74
x = 74 - 24
x = 50

Therefore, the person counted 50 humans and 24 horses.