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:

$k_{1}=\dfrac{ 7 }{ 7+6+4 }=\dfrac{ 7 }{ 17 } \doteq 0.4118 \ \\ k_{2}=\dfrac{ 6 }{ 7+6+4 }=\dfrac{ 6 }{ 17 } \doteq 0.3529 \ \\ k_{3}=\dfrac{ 4 }{ 7+6+4 }=\dfrac{ 4 }{ 17 } \doteq 0.2353 \ \\ \ \\ t=286000 \ \\ \ \\ z=t/(k_{1}+k_{2})=286000/(0.4118+0.3529)=374000 \ \\ a=z \cdot \ k_{1}=374000 \cdot \ 0.4118=154000$

$b=z \cdot \ k_{2}=374000 \cdot \ 0.3529=132000$

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

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