Kittens and chickens were running around the yard together, they had 14 heads and 38 legs, how many? - briefly
Let's analyze the problem by considering the number of heads and legs each animal has. Kittens have 1 head and 4 legs, while chickens have 1 head and 2 legs. To solve this, we need to determine the combination of kittens and chickens that results in 14 heads and 38 legs. Let's denote the number of kittens as K and the number of chickens as C. We can set up the following equations based on the given information:
- K + C = 14 (since each animal has one head)
- 4K + 2C = 38 (since kittens have 4 legs and chickens have 2 legs)
Solving these equations, we find that there are 5 kittens and 9 chickens. The solution involves solving a system of linear equations to find the exact numbers of kittens and chickens. The answer is 5 kittens and 9 chickens.
Kittens and chickens were running around the yard together, they had 14 heads and 38 legs, how many? - in detail
To determine the number of kittens and chickens in the yard, we need to analyze the given information about the total number of heads and legs. We start with the fact that there are 14 heads and 38 legs in total. Each animal, whether a kitten or a chicken, has one head. Therefore, the total number of animals is 14. Kittens and chickens have different numbers of legs: kittens have 4 legs, and chickens have 2 legs.
Let's denote the number of kittens as K and the number of chickens as C. We can set up the following system of equations based on the given information:
-
The total number of animals (heads): K + C = 14
-
The total number of legs: 4K + 2C = 38
We need to solve this system of equations to find the values of K and C. First, we can express C in terms of K from the first equation:
C = 14 - K
Next, we substitute this expression for C into the second equation:
4K + 2(14 - K) = 38 4K + 28 - 2K = 38 2K + 28 = 38 2K = 10 K = 5
Now that we have the number of kittens (K = 5), we can find the number of chickens (C) using the first equation:
C = 14 - K C = 14 - 5 C = 9
Therefore, there are 5 kittens and 9 chickens in the yard. This solution is derived from the given data and the biological facts about the number of legs that kittens and chickens possess.