A farm rears 9 ducks and cows in his farm. There are 28 legs altogether.How many ducks are there in the farm?
d + c = 9
2d + 4c = 28
Multiply the top equation by -2 and add. This will give you the number of cows. Find the ducks by substituting into the first equation.
let d=number of ducks reared
c=number of cows reared
sum of ducks and cows=d+c=9
sum of their legs=2d+4c=28 since duck has two legs and cow also has 4 legs
the two equations give
d+c=9...1
2d+4c=28...2
multiply eqn 1 by 2
2(d+c=9) which gives 4d+4c=18..3
now 2d+4c=28
-2d+2c=18
we have 2c=10
therefore c=5 put c into eqn..1
to get d+5=9
d=4 meaning there are 4 ducks and 5 cows.proof2*4=8legs in all does 4 ducks and 4*5=20 legs in all does 5 cows.
Let's assume that all the animals on the farm are either ducks or cows.
Let's say the number of ducks is represented by 'D' and the number of cows is represented by 'C'.
Each duck has 2 legs, so the total number of legs from ducks is 2D.
Each cow has 4 legs, so the total number of legs from cows is 4C.
Given that there are 28 legs altogether, we can set up the following equation:
2D + 4C = 28
We also know that there are 9 ducks and cows in total, so we can write another equation:
D + C = 9
We can now use these two equations to solve for the number of ducks (D).
First, let's solve the second equation for C:
C = 9 - D
Now substitute this value of C into the first equation:
2D + 4(9 - D) = 28
Simplifying the equation gives us:
2D + 36 - 4D = 28
Combining like terms gives us:
-2D + 36 = 28
Subtracting 36 from both sides:
-2D = -8
Dividing both sides by -2:
D = 4
Therefore, there are 4 ducks on the farm.
To determine the number of ducks on the farm, we can set up a system of equations based on the given information.
Let's assume that the number of ducks is represented by the variable "D" and the number of cows is represented by the variable "C".
Since each duck has 2 legs and each cow has 4 legs, we can set up the equation:
2D + 4C = 28 (equation 1)
Based on the statement, it is also given that there are a total of 9 ducks and cows, so we have the equation:
D + C = 9 (equation 2)
To solve this system of equations, we can use the substitution method.
First, let's solve equation 2 for one variable. Let's isolate "C":
C = 9 - D
Now, substitute this value of C into equation 1:
2D + 4(9 - D) = 28
Simplify the equation:
2D + 36 - 4D = 28
-2D + 36 = 28
-2D = 28 - 36
-2D = -8
Dividing both sides of the equation by -2:
D = -8 / -2
D = 4
Therefore, there are 4 ducks in the farm.