# 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.

Result

a =  154000
b =  132000
c =  88000

#### Solution:

$k_{ 1 } = \dfrac{ 7 }{ 7+6+4 } = \dfrac{ 7 }{ 17 } \doteq 0.4118 \ \\ k_{ 2 } = \dfrac{ 6 }{ 7+6+4 } = \dfrac{ 6 }{ 17 } \doteq 0.3529 \ \\ k_{ 3 } = \dfrac{ 4 }{ 7+6+4 } = \dfrac{ 4 }{ 17 } \doteq 0.2353 \ \\ \ \\ t = 286000 \ \\ \ \\ z = t/(k_{ 1 }+k_{ 2 }) = 286000/(0.4118+0.3529) = 374000 \ \\ a = z \cdot \ k_{ 1 } = 374000 \cdot \ 0.4118 \doteq 154000 = 154000$
$b = z \cdot \ k_{ 2 } = 374000 \cdot \ 0.3529 \doteq 132000 = 132000$
$c = z \cdot \ k_{ 3 } = 374000 \cdot \ 0.2353 = 88000$

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#### Following knowledge from mathematics are needed to solve this word math problem:

Need help calculate sum, simplify or multiply fractions? Try our fraction calculator. Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

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