Question

A soma de três números e 380 calcule-os sabendo que são inversamente proporcionais aos números 2 5 4

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Answer 1

$Ola'~~~\mathbb{FERNANDA} \\ \\ Sejam~os~tr\^es ~n\acute{u}meros~\begin{cases}x \\ y \\ z\end{cases} \\ \\ Nos~indica~que: \\ \underbrace{A~soma~de~tr\^es~n\acute{u}meros}_{x+y+z}~\underbrace{e'}_{=}~380 \\ \\ \boxed{x+y+z=380} \\ \\ \mathbb{tttttttttttttttttttttttttttttttttttttt} \\ E~indica~tamb\acute{e}m, que~s\~ao~inverseamente~a~os~n\acute{u}meros~2;5~e~4 \\ \frac{1}{2}~,~ \frac{1}{5}~,~ \frac{1}{4} \\ \\ \frac{10}{20}~, \frac{4}{20}~,~ \frac{5}{20}$


$\frac{x}{10}= \frac{y}{4}= \frac{z}{5}= \frac{\overbrace{x+y+z} ^{380} }{10+4+5} = \frac{380}{19}=20 \\ \\ \frac{x}{10}=20=\ \textgreater \ x=20.(10)=\boxed{x=200} \\ \\ \frac{y}{4}=20=\ \textgreater \ y=20.(4)=\boxed{y=80} \\ \\ \frac{z}{5}=20=\ \textgreater \ z=20.(5)=\boxed{z=100} \\ \\ \mathbb{iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii}\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Espero~ter~ajudado!!$