To solve this problem, we are going to use a system of equations. Let the variable c represent the number of chickens in the farm yard and the variable p represent the number of pigs in the farm yard. If there is a total of 70 heads, this means that the total number of animals (chickens plus pigs) must be 70. This can be represent by the equation: c + p = 70. We are also told that there are 200 legs. Using our knowledge that chickens have 2 legs and pigs have 4 legs, we can construct the following equation: 2c + 4p = 200. Our system of equations is as follows:
c + p = 70
2c + 4p = 200
To solve, we are going to subtract c from both sides of the first equation so that we can get the variable p alone. Then, using this value for p in terms of c, we are going to substitute into the second equation. This method is shown below:
c + p = 70
p = 70 - c
2c + 4p = 200
2c + 4(70-c) = 200
To solve this equation, we are first going to distribute the coefficient of 4 through the parentheses on the left side of the equation to simplify.
2c + 280 - 4c = 200
Next, we are going to combine like terms on the left side of the equation. This means adding together the two terms that both have a variable c.
-2c + 280 = 200
Next, we are going to subtract 280 from both sides of the equation so that we can move all of the constant (number only) terms to the right side of the equation.
-2c = -80
Finally, we are going to divide both sides of the equation by -2 to get the variable c alone.
c = 40
We should now substitute this value for c back into one of our original equations to solve for p.
c + p = 70
40 + p = 70
To solve, simply subtract 40 from both sides of the equation to get the variable p alone.
p = 30
Therefore, your answer is that there were 40 chickens and 30 pigs.
Hope this helps!
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