King of Bohemia

King of Bohemia Charles IV divided the entire family wealth among all his descendants. Wenceslas IV received 5/18, his younger brother Sigismund of Luxembourg received 1/9 less from his father than Wenceslas IV. Jan Zhorelecki was assigned 6/63. Which of these three brothers received the largest share of the wealth? How much of the wealth was divided among the other descendants?

Correct answer:

x = Vaclav
r =  431/1134

Step-by-step explanation:

$$\begin{gathered} V=\frac{5}{18}\doteq 0.2778 \\ Z=V-V/9=\frac{5}{18}-\frac{5}{18}/9=\frac{20}{81}\doteq 0.2469 \\ J=6/63=\frac{2}{21}\doteq 0.0952 \\ V>Z>J \\ x=Vaclav \end{gathered}$$

$$\begin{gathered} s=V+Z+J=\frac{5}{18}+\frac{20}{81}+\frac{2}{21}=\frac{315}{1134}+\frac{280}{1134}+\frac{108}{1134}=\frac{315+280+108}{1134}=\frac{703}{1134}\doteq 0.6199 \\ r=1-s=1-0.6199=\frac{431}{1134}=0.3801 \end{gathered}$$

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