Question

1.fortniteOne day, a person went to a horse racing area. Instead of counting the number of humans and horses, he counted 74 heads and 196 legs. How many humans and horses were there?

A.
37 humans and 98 horses

B.
24 horses and 50 humans

C.
31 horses and 74 humans

D.
24 humans and 50 horses

Answer 1

B. 24 horses; 50 humans

Explanation:

Let h = number of humans

Let r = number of horses

A human has 1 head and 2 legs. h humans have h heads and 2h legs.

A horse has 1 head and 4 legs. r horses have r heads and 4r legs.

Equation for number of heads:

h + r = 74

Equation for number of legs:

2h + 4r = 196

Now we solve the following system of equations.

h + r = 74

2h + 4r = 196

Multiply the first equation by -2 to get:

-2h - 2r = -148

Add this equation to the original second equation:

2r = 48

r = 24

Now we use the first original equation and solve for h.

h + r = 74

h + 24 = 74

h = 50

Answer: 24 horses; 50 humans