While visiting a farm, you notice that there are only chickens and rabbits in the farmyard. You can't help but wonder how many of each animal there is on the yard, but when you ask Farmer Fred he refuses to give you a direct answer. (Some say he must have been a math teacher before he became a farmer.) Fred says that there are 18 heads and 58 feet in the yard (not including themselves) Assuming there are no mutant animals how many chickens and rabbits are in the yard?

Okay, 18 heads = 18 animals my question is how do I go about finding this?

Should I just do it randomly? Like first try 16 chickens and go on from there? Surely there is a simpler way to do this since a bigger problem wouldn't work this way.

let the number of chickens be x

and the number of rabbits be y

so x+y = 18 and 2x + 4y = 58, divide this last equation by 2 to get x+2y=29

then
x+2y=29
x+ y=18 ..... subtract them
y=11, subbing back x = 7

7 chicken and 11 rabbits

check: 18 animals, so 18 heads
7chicken have 14 feet, 11 rabbits have 44 feet, so 14+44 = 58 feet

Thank you!!

There are 7 chickens- 14 Chicken feet.

There are 11 rabbits- 44 chicken feet.

To solve this problem, you can use a system of equations based on the information given. Let's assign variables to represent the number of chickens and rabbits in the yard.

Let's say the number of chickens is represented by 'c' and the number of rabbits is represented by 'r'. Since each animal has one head, the total number of heads in the yard is 'c + r' which is equal to 18.

Since chickens have 2 feet and rabbits have 4 feet, we can calculate the total number of feet in the yard. The number of chicken feet is '2c' and the number of rabbit feet is '4r'. So, the total number of feet is '2c + 4r', which is equal to 58.

Now we have a system of equations:
Equation 1: c + r = 18 (number of heads equation)
Equation 2: 2c + 4r = 58 (number of feet equation)

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

Multiply Equation 1 by 2 to make the coefficients of 'c' equal in both equations:
2(c + r) = 2(18)
2c + 2r = 36

Now, subtract this equation from Equation 2 to eliminate 'c':
(2c + 4r) - (2c + 2r) = 58 - 36
2r = 22
r = 11

Substitute the value of 'r' back into Equation 1 to find 'c':
c + 11 = 18
c = 7

So, there are 7 chickens and 11 rabbits in the yard.

By solving the system of equations, we were able to determine the number of each animal in the farmyard.