Question

Farmer Jack has chickens, cows, and horses on his farm. Altogether, there are 24 heads and 74 feet. If Farmer Jack has two more horses than cows, how many of each animal does he have?

Answer 1

Answer:

Mistake in question, if there were 25 heads, then there are

13 chickens, 5 cows, 7 horses

Step-by-step explanation:

System of Equations

Let's call x=number of chickens, y=number of cows, z=number of horses

We know Jack has two more horses than cows, so

z=y+2

We also know there are 24 heads, one per animal, so

x+y+z=24

Combining with the previous condition:

x+y+y+2=24

x+2y=22

We finally know there are 74 feet, two for each chicken and four for each cow or horse:

2x+4y+4z=74

Combining with the first condition

2x+4y+4(y+2)=74

2x+4y+4y+8=74

2x+8y=66

Dividing by 2

x+4y=33

Let's bring the first equation here

x+2y=22

Subtracting both

2y=11

It would give us a decimal number of cows

y=5.5

And a decimal number of horses

z=7.5

And a integer number of chickens

x=22-11=11

If the number of heads would have been 25, our problem will be correctly stated and the answer would be

13 chickens, 5 cows, 7 horses