There are 18 animals in the farm. Some ar chickens and some are cows. I counted 50 legs in all. How many of the animals are cows and how many are chickens?
K+C=18
2K+4C=50
Can someone help me to solve this problem. Thank you.
you can easily see that K = 18-C
So, put that into the 2nd equation and you have
2(18-C)+4C = 50
36-2C+4C = 50
2C = 14
C = 7
So, K = 11
To solve this problem, we can use a system of equations to represent the given information. Let's assign variables to the number of chickens and cows on the farm.
Let's say the number of chickens is C, and the number of cows is K. Since we know that there are a total of 18 animals on the farm, we can write the first equation as:
C + K = 18 (equation 1)
Furthermore, since chickens have 2 legs and cows have 4 legs, we can determine the number of legs by multiplying the number of each animal by the number of legs they have. We also know that there are a total of 50 legs on the farm, which gives us the second equation:
2C + 4K = 50 (equation 2)
Now, we can solve this system of equations. We can use the method of substitution or elimination to find the values of C and K.
Let's use the substitution method. Solve equation 1 for C:
C = 18 - K
Now, substitute this expression for C in equation 2:
2(18 - K) + 4K = 50
Expand and simplify:
36 - 2K + 4K = 50
36 + 2K = 50
2K = 50 - 36
2K = 14
Divide both sides of the equation by 2:
K = 7
Now, substitute the value of K back into equation 1 to find C:
C + 7 = 18
Subtract 7 from both sides of the equation:
C = 18 - 7
C = 11
Therefore, there are 11 chickens and 7 cows on the farm.