Grandmother

Michael's grandmother raises chickens and rabbits. Michael calculated that they have a total of 20 heads and 64 legs. How many animals does Grandma keep?

Correct answer:

s =  8
k =  12

Step-by-step explanation:

$$\begin{gathered} s+k=20 \\ 2s+4k=64 \\ s+k=20 \\ 2\cdot s+4\cdot k=64 \\ k+s=20 \\ 4k+2s=64 \\ Pivot:Row1\leftrightarrow Row2 \\ 4k+2s=64 \\ k+s=20 \\ Row2-\frac{1}{4}\cdot Row1\to Row2 \\ 4k+2s=64 \\ 0.5s=4 \\ s=\frac{4}{0.5}=8 \\ k=\frac{64-2s}{4}=\frac{64-2\cdot 8}{4}=12 \\ k=12 \\ s=8 \end{gathered}$$

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