Skateboard

Petr wanted to buy a skateboard but 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 other two. His younger brother gave him 1,000 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:

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

Try another example