The number of dogs and chickens on a farm add up to 14. The number of legs between them is 36. How many dogs and how many chickens are on the farm if there are at least twice as many chickens as dogs
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Let's solve this problem step by step to find the number of dogs and chickens on the farm.
Let's assume the number of dogs on the farm is represented by the variable 'd', and the number of chickens is represented by the variable 'c'.
According to the problem statement, the number of dogs and chickens on the farm add up to 14. Mathematically, we can write this as:
d + c = 14 ...........(1)
Next, we know that the total number of legs between the dogs and chickens is 36. Dogs have 4 legs each, and chickens have 2 legs each. Mathematically, the total number of legs can be represented as:
4d + 2c = 36 ...........(2)
Lastly, the problem states that there are at least twice as many chickens as dogs, which can be expressed as:
c >= 2d ...........(3)
To solve this system of equations, we can use substitution or elimination.
Let's rearrange equation (1) to solve for d:
d = 14 - c
Substituting this into equation (2), we get:
4(14 - c) + 2c = 36
56 - 4c + 2c = 36
-2c = 36 - 56
-2c = -20
c = -20 / -2
c = 10
Substituting the value of c = 10 back into equation (1), we can find the value of d:
d + 10 = 14
d = 14 - 10
d = 4
Therefore, there are 4 dogs and 10 chickens on the farm.