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?

Question

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?

is the answer -

Let's assume that HM = Human and
HR = Horse

HM + HR = 74
2HM + 4HR = 196
(2HM + 4HR) - (2 HM + 2HR) = 196 - 148
2HR = 48
HR = 24
HM + (24) = 74
HM = 74 - 24
HM = 50

So, the solution is 24 horses and 50 humans.

is that correct

yes, and it checks. The best way to check these is go back and see if it works in the problem statement.

Answer 1

Yes, the answer is correct. The person was able to determine the number of humans and horses by setting up a system of equations based on the total number of heads and legs.

Let's break it down step by step:

First, the person counts 74 heads, which represents the total number of humans and horses combined. So, we can represent this as HM (number of humans) plus HR (number of horses) equals 74:

HM + HR = 74

Next, the person counts 196 legs, which means there are 2 legs for every human and 4 legs for every horse. So, the equation becomes:

2HM + 4HR = 196

To solve this system of equations, we can use a method called "substitution" or "elimination." In this case, let's use the elimination method.

We want to eliminate the "HM" variable from the second equation, so we can multiply the first equation by 2:

2(HM + HR) = 2(74)
2HM + 2HR = 148

Now, we can subtract the second equation from the first equation to eliminate the "HM" variable:

(2HM + 4HR) - (2HM + 2HR) = 196 - 148
2HR = 48

Dividing both sides of the equation by 2, we get:

HR = 24

So, the number of horses is 24.

Now, we can substitute the value of HR back into the first equation to find the number of humans:

HM + 24 = 74
HM = 74 - 24
HM = 50

Therefore, there are 50 humans and 24 horses in total.

To check if the solution is correct, we can plug in these values into the original equations:

50 humans + 24 horses = 74 (correct)

2(50) + 4(24) = 196 (correct)

Both equations are true, so the solution of 50 humans and 24 horses is correct.