1. 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?
im stuck.. please help
Horses+Humans=74
4Horses+2humans=<196
50x2 = 100 feet
24x4 = 96 feet
answer is 74 heads & 196 feet
To solve this problem, you can use a system of equations. Let's assume that the number of humans is 'H' and the number of horses is 'R'.
Now, let's consider the given information:
1. There are 74 heads in total. Since every human and horse has one head each, we can write the equation: H + R = 74.
2. There are 196 legs in total. Humans have two legs each, and horses have four legs each. So, the total number of legs can be expressed as 2H + 4R = 196.
Now, we have two equations with two variables. We can solve this system of equations simultaneously to find the values of H and R.
Using substitution or elimination method, we can solve this system of equations. Here's the solution:
Equation 1: H + R = 74
Equation 2: 2H + 4R = 196
Multiplying Equation 1 by 2, we get:
2H + 2R = 148
Subtracting this result from Equation 2, we get:
2H + 4R - (2H + 2R) = 196 - 148
2R = 48
R = 48/2
R = 24
Now that we know the value of R, we can substitute it back into Equation 1 to find the value of H:
H + R = 74
H + 24 = 74
H = 74 - 24
H = 50
Therefore, there are 50 humans and 24 horses.