Question

A poultry farm has chickens and cows. When the caretaker of the poultry counted the heads of the stock in the farm, the number totalled up to 200. However, when the number of legs was counted, the number totalled up to 640. How many more cows were there in the farm?

Note: In the farm, each cow had 4 legs and each chicken had 2 legs.

A 60
B 40
C 120
D 80
E None of the above

Answer 1

To solve the question, two equations were set up based on the number of heads and legs. After performing algebraic operations, it was found that there are 40 more cows than chickens on the poultry farm.

Step-by-step explanation:

The student has asked a question involving a poultry farm with chickens and cows that requires the use of algebra to solve. When the caretaker counts heads, there are 200 heads in total. This can be translated to 200 animals on the farm. When the caretaker counts legs, there is a total of 640 legs. Since cows have 4 legs and chickens have 2, we can set up the following system of equations:

Let C represent the number of cows and Ch represent the number of chickens. We can establish the following equations:

1. C + Ch = 200 (heads)
2. 4C + 2Ch = 640 (legs)

By multiplying the first equation by 2, we get:

2C + 2Ch = 400

Subtracting this from the second equation (4C + 2Ch = 640), we find:

1. 2C = 240

This simplifies to C = 120, which means there are 120 cows. Substituting C into the first equation gives us Ch = 80. Hence, there are 80 chickens.
To find out how many more cows than chickens there are, we simply subtract the number of chickens from the number of cows:

120 cows - 80 chickens = 40 more cows

Therefore, the answer is B,40 more cows in the farm than chickens.