There are 42 goats and chickens in the farm.there are 114 legs altogether.how many ducks are there?
ducks?
To solve this problem, let's start by assigning variables to the number of goats, chickens, and ducks. Let "g" represent the number of goats, "c" represent the number of chickens, and "d" represent the number of ducks.
Based on the information given, we know that there are a total of 42 goats and chickens, so we can write the equation: g + c = 42.
Additionally, we know that there are a total of 114 legs on the farm. Since each goat and each chicken have 4 legs, and each duck has 2 legs, we can write the equation: 4g + 4c + 2d = 114.
Now, we need to solve this system of equations to find the values of "g," "c," and "d."
We can start by solving the first equation for one of the variables. Let's solve for "g" in terms of "c": g = 42 - c.
Now we substitute this value of "g" into the second equation: 4(42 - c) + 4c + 2d = 114.
Next, distribute the 4: 168 - 4c + 4c + 2d = 114.
Combine like terms: 168 + 2d = 114.
Subtract 168 from both sides: 2d = -54.
Divide both sides by 2: d = -27.
Since it doesn't make sense to have a negative number of ducks, there must be an error in the problem statement or calculations. Please recheck the information provided, and let me know if you have any further questions.