Question

A razão entre dois números é 57, e sua soma é 180. Quais os dois números?

Answer 1

$\large\begin{array}{l} \textsf{Se a soma dos dois n\'umeros \'e 180, podemos represent\'a-los}\\\textsf{como }\mathsf{x~e~(180-x).}\\\\\\ \textsf{A raz\~ao entre eles \'e igual a 57. Logo, deve-se ter}\\\\ \mathsf{\dfrac{x}{180-x}=57}\\\\ \mathsf{x=57\cdot (180-x)}\\\\ \mathsf{x=10\,260-57x}\\\\ \mathsf{x+57x=10\,260}\\\\ \mathsf{58x=10\,260} \end{array}$

$\large\begin{array}{l} \mathsf{x=\dfrac{10\,260}{58}\begin{array}{c}^{\mathsf{\div 2}}\\^{\mathsf{\div 2}} \end{array}}\\\\ \boxed{\begin{array}{c}\mathsf{x=\dfrac{5\,130}{29}} \end{array}} \end{array}$


$\large\begin{array}{l} \textsf{O outro n\'umero procurado \'e}\\\\ \mathsf{180-x=180-\dfrac{5\,130}{29}}\\\\ \mathsf{180-x=\dfrac{180\cdot 29}{29}-\dfrac{5\,130}{29}}\\\\ \mathsf{180-x=\dfrac{180\cdot 29}{29}-\dfrac{5\,130}{29}}\\\\ \mathsf{180-x=\dfrac{5\,220}{29}-\dfrac{5\,130}{29}}\\\\ \boxed{\begin{array}{c}\mathsf{180-x=\dfrac{90}{29}} \end{array}} \end{array}$


$\large\begin{array}{l} \textsf{Os n\'umeros procurados s\~ao }\mathsf{\dfrac{5\,130}{29}~e~\dfrac{90}{29}.} \end{array}$


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$\large\begin{array}{l} \textsf{D\'uvidas? Comente.}\\\\\\ \textsf{Bons estudos! :-)} \end{array}$


Tags: razão soma dois números sistema equações lineares proporção