If a farm as 13 heads and 36 feet. How many chicken are there and how many rabbit are there?
use a system of equations.
x+y=13
2x+4y=36
multiply first equation by negative two
-2x-2y=-26
2x+4y=36
then eliminate the x
2y=10
y=5
then solve for x
To find out the number of chickens and rabbits on the farm, we can use a system of equations based on the number of heads and feet.
Let's assume 'c' represents the number of chickens and 'r' represents the number of rabbits.
1) Determine the number of heads: Since each animal has one head, we can write the first equation as:
c + r = 13
2) Determine the number of feet: Each chicken has 2 feet, and each rabbit has 4 feet. So, the second equation is:
2c + 4r = 36
We can now solve this system of equations to find the values of 'c' and 'r'.
Using the first equation, we can rewrite it as c = 13 - r and substitute it into the second equation:
2(13 - r) + 4r = 36
26 - 2r + 4r = 36
2r = 10
r = 5
Using this value of 'r' in the first equation, we can find 'c':
c + 5 = 13
c = 8
Therefore, there are 8 chickens and 5 rabbits on the farm.
To determine the number of chickens and rabbits on the farm, we can use a system of equations. Let's assume that "x" represents the number of chickens and "y" represents the number of rabbits.
Since every animal has 1 head, the equation for the total number of heads can be written as:
x + y = 13 (Equation 1)
Rabbits have 4 feet, while chickens have 2 feet. So, the equation for the total number of feet can be written as:
2x + 4y = 36 (Equation 2)
Now, we can solve this system of equations to find the values of "x" and "y".
To solve Equation 1 for "x", we can subtract "y" from both sides:
x = 13 - y
Substituting this value of "x" into Equation 2, we get:
2(13 - y) + 4y = 36
Expanding and simplifying this equation:
26 - 2y + 4y = 36
2y = 36 - 26
2y = 10
y = 10/2
y = 5
Now that we have the value of "y" (which represents the number of rabbits), we can substitute it back into Equation 1 to find "x":
x + 5 = 13
x = 13 - 5
x = 8
Therefore, there are 8 chickens and 5 rabbits on the farm.