Gold inheritance

The king divided the inheritance with his three sons in the ratio of 7: 6: 4. Two of them received 286,000 gold. How much each of the sons got.

Correct result:

a =  154000
b =  132000
c =  88000

Solution:

$$\begin{gathered} k_1={\displaystyle \frac{7}{7+6+4}}={\displaystyle \frac{7}{17}}\doteq 0.4118 \\ {k}_2={\displaystyle \frac{6}{7+6+4}}={\displaystyle \frac{6}{17}}\doteq 0.3529 \\ {k}_3={\displaystyle \frac{4}{7+6+4}}={\displaystyle \frac{4}{17}}\doteq 0.2353 \\ t=286000 \\ z=t\mathrm{/}(k_1+k_2)=286000\mathrm{/}(0.4118+0.3529)=374000 \\ a=z\cdot k_1=374000\cdot 0.4118=154000 \end{gathered}$$

$b=z\cdot k_2=374000\cdot 0.3529=132000$

$c=z\cdot k_3=374000\cdot 0.2353=88000$

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