[tex] \it 2x=3y=8z\ \ \ \ \ \ (1)
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\dfrac{^{2)}1}{\ x} +\dfrac{^{3)}1}{\ y} +\dfrac{^{8)}1}{z} =\dfrac{13}{1200} \Rightarrow \dfrac{2}{2x} +\dfrac{3}{3y} +\dfrac{8}{8z} =\dfrac{13}{1200} \stackrel{(1)}{\Longrightarrow}
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\Rightarrow \dfrac{2}{2x} +\dfrac{3}{2x} +\dfrac{8}{2x} =\dfrac{13}{1200} \Rightarrow \dfrac{2+3+8}{2x} =\dfrac{13}{1200} \Rightarrow \dfrac{13}{2x} =\dfrac{13}{1200}\Rightarrow
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\Rightarrow 2x = 1200 \Rightarrow x = 1200:2 \Rightarrow x = 600 \ \ \ \ \ \ (2) [/tex]
[tex] \it (1), \ (2) \Rightarrow 1200=3y \Rightarrow y = 1200:3 \Rightarrow y = 400
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(1), \ (2) \Rightarrow 1200=8z \Rightarrow z = 1200:8 \Rightarrow z = 150 [/tex]
