Divide 8

Divide 6840 by x y and z, in such a way that x has twice as much as y, who has half as much as z

Correct answer:

x =  2736
y =  1368
z =  2736

Step-by-step explanation:

$$\begin{gathered} 6840=x+y+z \\ x=2y \\ 2y=z \\ 6840=x+(x\mathrm{/}2)+(2y) \\ 6840=x+(x\mathrm{/}2)+x \\ 6840=x+(x\mathrm{/}2)+x \\ 5x=13680 \\ x=2736 \end{gathered}$$

$y=x\mathrm{/}2=2736\mathrm{/}2=1368$

$z=2\cdot y=2\cdot 1368=2736$

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