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
c >= 2d
c+d = 14
2c+4d = 36
2(14 - d) + 4d = 36
28 + 2d = 36
2d = 8
d = 4
so, c = 10
the bit about c>=2d is redundant and unnecessary.
To solve this problem, let's assign variables to the number of dogs and chickens on the farm. Let's say "d" represents the number of dogs and "c" represents the number of chickens.
We are given two conditions:
1. The sum of the number of dogs and chickens is 14: d + c = 14
2. The total number of legs between them is 36: 4d + 2c = 36 (each dog has 4 legs, and each chicken has 2 legs)
Since there are at least twice as many chickens as dogs, we can write another equation: c ≥ 2d.
Now, we have a system of equations:
1. d + c = 14
2. 4d + 2c = 36
3. c ≥ 2d
To solve this system, we can use substitution or elimination. Let's use substitution:
From equation 3, we can rewrite it as c - 2d ≥ 0. This inequality tells us that c must be greater than or equal to 2d.
Now, we can solve equation 3 for c: c ≥ 2d.
Let's substitute this into equation 1: d + (2d) = 14
Simplifying, we get: 3d = 14
Dividing both sides by 3: d = 14/3 ≈ 4.67
Since the number of dogs must be a whole number, we round down: d = 4.
Now, substitute d = 4 back into equation 1 to find c: 4 + c = 14
Simplifying, we get: c = 14 - 4 = 10
Therefore, there are 4 dogs and 10 chickens on the farm.