a)
[tex]\it \dfrac{x}{3}=\dfrac{y}{4} \ \ \ \ (1)
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\dfrac{y}{4}=\dfrac{z}{5} \ \ \ \ (2)
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(1), (2) \Rightarrow \dfrac{x}{3}=\dfrac{y}{4} =\dfrac{z}{5} =k \Rightarrow \begin{cases}\it x = 3k
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\it y=4k
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\it z = 5k\end{cases} \ \ \ \ (*)[/tex]
[tex]\it x\cdot y\cdot z=480 \stackrel{(*)}{\Longrightarrow}3k\cdot4k\cdot5k = 480 \Rightarrow 60\cdot k\cdot k\cdot k=480|_{:60} \Rightarrow
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\Rightarrow k\cdot k\cdot k= 8 \Rightarrow k\cdot k\cdot k= 2\cdot2\cdot2 \Rightarrow k=2\stackrel{(*)}{\Longrightarrow} \begin{cases}\it x = 3\cdot2=6
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\it y=4\cdot2=8
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\it z = 5\cdot2=10\end{cases}[/tex]
