Horses and hens

In a park, there are some horses and some hens. If the total number of heads is 68 and the total number of legs is 198, find the number of hens in the park.

Final Answer:

a =  37

Step-by-step explanation:

$$\begin{gathered} a+b=68 \\ 2a+4b=198 \\ 2\cdot a+4\cdot b=198 \\ a+b=68 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ -b=-31 \\ b=\frac{-31}{-1}=31 \\ a=\frac{198-4b}{2}=\frac{198-4\cdot 31}{2}=37 \\ a=37 \\ b=31 \end{gathered}$$

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