14 heads and 38 legs - how many kittens and chickens? - briefly
To solve the problem of determining the number of kittens and chickens given 14 heads and 38 legs, we start by noting that each kitten has 1 head and 4 legs, while each chicken has 1 head and 2 legs. By setting up a system of linear equations, we can express the total number of heads and legs in terms of the number of kittens (k) and chickens (c). The equations are:
- k + c = 14 (total heads)
- 4k + 2c = 38 (total legs)
Solving these equations, we find that there are 6 kittens and 8 chickens.
14 heads and 38 legs - how many kittens and chickens? - in detail
To determine the number of kittens and chickens given that there are 14 heads and 38 legs, we need to establish the characteristics of kittens and chickens. Kittens have 1 head and 4 legs, while chickens have 1 head and 2 legs. We can set up a system of linear equations to solve for the number of kittens (let's denote this as K) and chickens (denote this as C).
First, we know that the total number of heads is 14. Since each kitten and each chicken have one head, we can write the equation: K + C = 14
Next, we know that the total number of legs is 38. Kittens have 4 legs, and chickens have 2 legs, so we can write the equation: 4K + 2C = 38
Now, we have a system of two equations:
- K + C = 14
- 4K + 2C = 38
To solve this system, we can use the substitution or elimination method. Let's use the elimination method. First, we can multiply the first equation by 2 to align the coefficients of C: 2K + 2C = 28
Now, we subtract this new equation from the second equation: (4K + 2C) - (2K + 2C) = 38 - 28 2K = 10 K = 5
Now that we have the value of K, we can substitute it back into the first equation to find C: K + C = 14 5 + C = 14 C = 14 - 5 C = 9
Therefore, there are 5 kittens and 9 chickens. This solution is derived from the given data and the biological characteristics of kittens and chickens. The steps involve setting up and solving a system of linear equations, ensuring that the solution is both mathematically and biologically accurate. This method provides a clear and precise way to determine the number of kittens and chickens based on the given information.