D + C = 12 (number of heads)
2D + 4C = 32 (number of feet)
Solve for D and C, using algebra.
2D + 4C = 32 (number of feet)
Solve for D and C, using algebra.
so my answer is 4 cows and 8 ducks
D + C = 12
8 + 4 = 12
2 D + 4 C = 32
2(8)+ 4(4)= 32
16 + 16 = 32
32 = 32
We know that ducks have 1 head and 2 feet, while cows have 1 head and 4 feet. We can use this information to set up the following equations:
Equation 1: D + C = 12
This equation represents the total number of heads, which is the sum of the ducks and cows.
Equation 2: 2D + 4C = 32
This equation represents the total number of feet, which is the sum of the feet of ducks and cows.
Now, we can solve this system of equations to find the values of D and C. Let's start by solving equation 1 for D:
D = 12 - C
Next, substitute this value of D into equation 2:
2(12 - C) + 4C = 32
Simplify:
24 - 2C + 4C = 32
Combine like terms:
2C = 8
Divide both sides by 2:
C = 4
Now, substitute this value of C into equation 1 to find D:
D + 4 = 12
D = 12 - 4
D = 8
Therefore, there were 8 ducks and 4 cows on the farm.