A farmer raises cows and chickens. The farmer has a total of 21 animals. One day he counts the legs of all his animals and realizes he has a total of 62 legs. How many of each animal does he have?
4 w + 2 k = 62
w + k = 21
solve using substitution
... or elimination
say that all 21 are chickens. That would give 42 legs.
Each chicken that is replaced with a cow will raise the leg count by 2.
we have 20 extra legs, so that means we need 10 cows.
Thus, 11 chickens, 10 cows
Let's assume that the farmer has x cows and y chickens.
Since the farmer has a total of 21 animals, we can write the equation:
x + y = 21 ---(equation 1)
Cows have 4 legs, and chickens have 2 legs. Therefore, the total number of legs can be expressed as:
4x + 2y = 62 ---(equation 2)
To solve these equations, we can use the substitution method or the elimination method. Let's use the elimination method.
Multiplying equation 1 by 2, we get:
2x + 2y = 42 ---(equation 3)
Now, we'll subtract equation 3 from equation 2:
(4x + 2y) - (2x + 2y) = 62 - 42
2x = 20
x = 10
Substituting the value of x back into equation 1, we can find y:
10 + y = 21
y = 11
Therefore, the farmer has 10 cows and 11 chickens.
To determine the number of cows and chickens the farmer has, we can set up a system of equations based on the given information.
Let's denote the number of cows as 'C' and the number of chickens as 'K'.
From the information provided, we know that the farmer has a total of 21 animals, so we can write the equation: C + K = 21.
We also know that the total number of legs on the farm is 62. Since cows have 4 legs and chickens have 2 legs, we can write the equation: 4C + 2K = 62.
Now, we can solve this system of equations to find the values for C and K.
First, let's solve the first equation for C:
C = 21 - K.
Now, substitute this value of C into the second equation:
4(21 - K) + 2K = 62.
Simplifying the equation:
84 - 4K + 2K = 62.
-2K = 62 - 84.
-2K = -22.
Dividing by -2:
K = -22 / -2.
K = 11.
Now that we have the value of K, we can substitute it back into the first equation to find C:
C + 11 = 21,
C = 21 - 11,
C = 10.
Therefore, the farmer has 10 cows and 11 chickens.