Skateboard

Petr wanted to buy a skateboard. But he had no money, so he asked his father and two brothers for help. His father gave him half of the amount his brothers gave him. His older brother gave him a third of what he received from the others. His younger brother gave him 1000 CZK. The donated
amount exactly covered the purchase of the skateboard. How much did the skateboard cost?

Final Answer:

x =  2400 Kc

Step-by-step explanation:

$$\begin{gathered} o=(a+b)/2 \\ a=(o+b)/3 \\ b=1000 \\ a+b-2o=0 \\ 3a-b-o=0 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{3}\cdot Row1\to Row2 \\ 1.333b-1.667o=0 \\ Row3-\frac{1}{1.33333333}\cdot Row2\to Row3 \\ 1.25o=1000 \\ o=\frac{1000}{1.25}=800 \\ b=\frac{0+1.6666666666667o}{1.33333333}=\frac{0+1.66666667\cdot 800}{1.33333333}=1000 \\ a=\frac{0+b+o}{3}=\frac{0+1000+800}{3}=600 \\ a=600 \\ o=800 \\ x=o+a+b=800+600+1000=2400\text{Kc} \end{gathered}$$

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