A human has 1 head and 2 legs.
A horse has 1 head and 4 legs.
Let's make two equations from what we know.
There were a total of 74 heads.
There were a total of 196 legs.
Let's call humans 'x' and horses 'y'
The total number of heads were 74.
Humans have 1 head, and so do horses.
Our first equation is:
x + y = 74
There were a total of 196 legs.
Humans have 2 legs, and horses have 4 legs.
Our second equation is:
2x + 4y = 196
Our two equations are:
x + y = 74
2x + 4y = 196
We need to solve this system of equations to find out how many humans and horses were at this racing event.
Multiply the first equation by 2.
2(x + y) = 2(74)
2x + 2y = 148
Our two equations are:
2x + 2y = 148
2x + 4y = 196
Subtract the first equation from the second equation.
2x - 2x + 2y - 4y = 148 - 196
2y - 4y = 148 - 196
-2y = - 48
Divide both sides by -2
y = 24
That means that there were 24 horses.
We can plug back in y = 24 into our first equation to find out how many humans there were.
x + y = 74
x + 24 = 74
x + 24 - 24 = 74 - 24
x = 50
There were 50 humans.
At the horse racing event, there were 24 horses and 50 humans.
Your final answer is B. 24 horses and 50 humans.
