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?
2H+4Horse=196
H+Horse=74
solve by substitution
To solve this problem, we can use a system of equations. Let's assume the number of humans is represented by 'H' and the number of horses is represented by 'R'.
The person counted 74 heads, which means the total number of humans and horses is 74. Therefore, we can write the equation: H + R = 74 (Equation 1).
The person also counted 196 legs, which means humans have 2 legs each and horses have 4 legs each. Using this information, we can write another equation: 2H + 4R = 196 (Equation 2).
Now, we have two equations with two variables.
To solve them simultaneously, we can use a method called substitution. Solve Equation 1 for H in terms of R: H = 74 - R.
Substitute this expression into Equation 2:
2(74 - R) + 4R = 196.
Now let's solve this equation to find R:
148 - 2R + 4R = 196,
2R = 48,
R = 24.
So, there are 24 horses.
To find the number of humans, substitute the value of R into Equation 1:
H + 24 = 74,
H = 50.
Therefore, there are 50 humans.
In conclusion, there are 50 humans and 24 horses at the horse racing area.