A farm rears 9 ducks and cows in his farm. There are 28 legs altogether.How many ducks are there in the farm?
2d+4(9-d) = 28
d = 4
4 ducks, 5 cows
To determine the number of ducks on the farm, we need to solve a system of equations based on the given information.
Let's use the variables 'D' to represent the number of ducks and 'C' to represent the number of cows.
1. Each duck has 2 legs, so the total number of duck legs is 2D.
2. Each cow has 4 legs, so the total number of cow legs is 4C.
3. The total number of legs is given as 28, so we can write the equation: 2D + 4C = 28.
Now, we also know that the farm rears a total of 9 ducks and cows, which we can express as: D + C = 9.
To solve this system of equations, we can use substitution or elimination method:
Let's solve using substitution method:
1. Solve the second equation for C: C = 9 - D.
2. Substitute this expression for C into the first equation:
2D + 4(9 - D) = 28.
Simplify the equation: 2D + 36 - 4D = 28.
Combine like terms: -2D + 36 = 28.
Subtract 36 from both sides: -2D = -8.
Divide both sides by -2: D = 4.
Therefore, there are 4 ducks on the farm.