There are some rabbits and chickens in a farm. Together they have 35 heads and 94 feet. How many rabbits? How many chickens?
heads: r+c = 35
feet: 4r+2c = 94
Now just solve for r and c, in any of several ways.
1. Think about it, if all the chickens raise one of their legs, and the rabbits raise two of their legs, then it's 94/2=47.
2. So if there's even one rabbit in the cage, the number of legs will have one more than the number of heads for each rabbit there are.
3. So you subtract the half amount of legs by the number of heads, and it's 47-35=12, so there are 12 rabbits in the cage.
4. If there are 12 rabbits in the cage, then 12 rabbits = 12 heads and 48, and so you subtract the total number of heads/legs from the number of heads/legs that belong to a rabbit, which is 94-48=46, and 35-12=23.
5. So there are 23 chickens and 12 rabbits.
r+c=76
To solve this problem, we can set up a system of equations.
Let's assume that the number of rabbits is represented by 'r' and the number of chickens is represented by 'c'.
We know that each rabbit has 1 head and 4 feet, and each chicken has 1 head and 2 feet. Using this information, we can create the following equations:
Equation 1: r + c = 35 (since the total number of heads is 35)
Equation 2: 4r + 2c = 94 (since the total number of feet is 94)
Now we can solve this system of equations using different methods, such as substitution or elimination.
Method 1: Substitution
- Rearrange Equation 1 to solve for r: r = 35 - c
- Substitute this expression for r in Equation 2: 4(35 - c) + 2c = 94
- Distribute and solve for 'c': 140 - 4c + 2c = 94
- Simplify: -2c = -46
- Divide both sides by -2: c = 23
Now, substitute the value of 'c' back into Equation 1 to find 'r':
r + 23 = 35
r = 35 - 23
r = 12
So, there are 12 rabbits and 23 chickens in the farm.