Boletus  and cossacks

Paul has 8 dry boletus, 1/2 less oak boletus, 5x more cossacks than butter mushrooms. He has 3x more cossacks and butter mushrooms together than dry boletus. How many mushrooms does he have in total? And how many butter mushrooms and how many cossacks?

Final Answer:

x =  36
m =  4
k =  20

Step-by-step explanation:

$$\begin{gathered} s=8 \\ d=s-s/2 \\ k=5m \\ k+m=3s \\ x=s+d+k+m \\ d=8-8/2 \\ k+m=3\cdot 8 \\ x=8+d+k+m \\ k=5\cdot m \\ 2d=8 \\ k-5m=0 \\ k+m=24 \\ d+k+m-x=-8 \\ Row4-\frac{1}{2}\cdot Row1\to Row4 \\ k+m-x=-12 \\ Row3-Row2\to Row3 \\ 6m=24 \\ Row4-Row2\to Row4 \\ 6m-x=-12 \\ Row4-Row3\to Row4 \\ -x=-36 \\ x=\frac{-36}{-1}=36 \\ m=\frac{24}{6}=4 \\ k=0+5m=0+5\cdot 4=20 \\ d=\frac{8}{2}=4 \\ d=4 \\ k=20 \\ m=4 \\ x=36 \end{gathered}$$

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