Kittens and chickens have 42 legs and 12 heads, how many kittens and chickens were there? - briefly
To determine the number of kittens and chickens, we need to use basic algebra. Let's denote the number of kittens as K and the number of chickens as C. Kittens have 4 legs and 1 head, while chickens have 2 legs and 1 head. The equations derived from the problem are:
- 4K + 2C = 42 (total legs)
- K + C = 12 (total heads)
Solving these equations, we find that there are 6 kittens and 6 chickens.
Kittens and chickens have 42 legs and 12 heads, how many kittens and chickens were there? - in detail
To determine the number of kittens and chickens based on the given information, we need to use a systematic approach involving basic arithmetic and logic. Let's denote the number of kittens as K and the number of chickens as C.
First, we establish the biological facts:
- Each kitten has 4 legs and 1 head.
- Each chicken has 2 legs and 1 head.
We are given two pieces of information:
- The total number of legs is 42.
- The total number of heads is 12.
From these, we can set up the following equations:
- For the legs: 4K + 2C = 42
- For the heads: K + C = 12
To solve these equations, we can use the substitution or elimination method. Let's use the substitution method. From the second equation, we can express C in terms of K:
C = 12 - K
Now, substitute C in the first equation:
4K + 2(12 - K) = 42
Simplify and solve for K:
4K + 24 - 2K = 42 2K + 24 = 42 2K = 42 - 24 2K = 18 K = 9
Now that we have the value of K, we can find C:
C = 12 - K C = 12 - 9 C = 3
Therefore, there are 9 kittens and 3 chickens. This solution is derived from the biological facts and the given data, ensuring an accurate and logical conclusion.