There are 38 animals at a farm .some are cows and some are chickens . All together there are 124legs. How many cows and how many chickens?
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To find the number of cows and chickens at the farm, we can set up a system of equations based on the given information.
Let's assume the number of cows is represented by 'c' and the number of chickens is represented by 'ch'.
1. First, let's set up an equation based on the total number of animals: c + ch = 38.
2. Then, we can set up an equation based on the total number of legs: 4c + 2ch = 124 (since cows have 4 legs and chickens have 2 legs).
Now, we can solve the system of equations to find the values of 'c' and 'ch'.
One way to solve this system is by substitution. Rearrange the first equation to solve for one variable. Let's solve for 'c':
c = 38 - ch.
Now, substitute this expression for 'c' in the second equation:
4(38 - ch) + 2ch = 124.
Simplify and solve for 'ch':
152 - 4ch + 2ch = 124,
-2ch = 124 - 152,
-2ch = -28,
ch = -28 / -2,
ch = 14.
Now, substitute the value of 'ch' back into the first equation to find 'c':
c + 14 = 38,
c = 38 - 14,
c = 24.
Therefore, there are 24 cows and 14 chickens at the farm.