farmer fred had chickens and cows on his farm. he knows that together there are 108 legs and 30 heads. how many of each type of animal does he have?
c chickens have 2c legs
m cows have 4m legs
c+m = 30
2c + 4m = 108
multiply the top equation by two, and subtract
2c + 2m = 60
2c + 4m = 108
2m = 48
m = 24
c = 6
To find out how many chickens and cows Farmer Fred has, we can set up a system of equations based on the given information.
Let's define:
C = Number of chickens
W = Number of cows
We know that each chicken has 2 legs and each cow has 4 legs. So, we can write the equation for the total number of legs:
2C + 4W = 108 -- Equation 1
We also know that the total number of heads is 30, which can be expressed as:
C + W = 30 -- Equation 2
Now, we can solve this system of equations to determine the values of C and W.
Earlier, Equation 2 can be rearranged as C = 30 - W. We substitute this expression for C into Equation 1:
2(30 - W) + 4W = 108
Distribute the 2 to both terms inside the parentheses:
60 - 2W + 4W = 108
Combine like terms:
2W = 108 - 60
2W = 48
W = 48/2
W = 24
We have found that Farmer Fred has 24 cows. To determine the number of chickens, we substitute this value for W back into Equation 2:
C + 24 = 30
C = 30 - 24
C = 6
Therefore, Farmer Fred has 6 chickens and 24 cows on his farm.