4 w + 2 k = 62
w + k = 21
solve using substitution
... or elimination
w + k = 21
solve using substitution
... or elimination
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
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.
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.