One day a person went to a hourse racing area,instead of counting the humans and the horses he instead counted the heads and leg there where 74 heads and 196 legs yet he still knew the number of the humans and the hourses.How did he figure that out and how many hourses and humans are there?
well let me check
24 hourses
50 humans
h = horses
p = people
h+p=74
4h + 2p = 196
h = 74-p
4(74-p) + 2p = 196
296 - 4p + 2p = 196
100 = 2p
50 = p
So ... yes. 50 humans. 24 horses. Good job.
Matt
To solve this problem, let's use a system of equations. Let's assume there are h horses and p humans.
1) We know that the total number of heads is 74, which includes both horses and humans. Therefore, the equation is:
h + p = 74
2) We also know that the total number of legs is 196, which includes both horse legs (4 legs per horse) and human legs (2 legs per person). Therefore, the equation is:
4h + 2p = 196
Now, let's solve these equations simultaneously using substitution or elimination.
First, let's isolate one variable in the first equation. For example, we can isolate h:
h = 74 - p
Now substitute this expression for h in the second equation:
4(74 - p) + 2p = 196
Simplify the equation:
296 - 4p + 2p = 196
Combine like terms:
-2p = -100
Divide both sides by -2:
p = 50
Now substitute the value of p back into the first equation to find h:
h + 50 = 74
h = 24
Therefore, there are 24 horses and 50 humans at the horse racing area.