Question

99 dividido por números inversamente proporcionais a 2,4e6

Answer 1

Dividindo 99  por números inversamente proporcionais a 2, 4 e 6

$\large 2 = 16,5 \\\\\large 4 = 33 \\\\\large 6 = 49,5$

                       $\large Grandezas~ inversamente~ proporcionais$

a = 2

b = 4

c = 6

$\large$$\large \text { \dfrac{a}{\dfrac{1}{2} } } = \large \text { \dfrac{b}{\dfrac{1}{4} } } = \large \text { \dfrac{c}{\dfrac{1}{6} } }\\\\\\\large \text { \dfrac{a}{\dfrac{2}{1} } } = \large \text { \dfrac{b}{\dfrac{4}{1} } } = \large \text { \dfrac{c}{\dfrac{6}{1} } }\\\\\\\large \dfrac{a}{2} = \large \dfrac{b}{4} = \large \dfrac{c}{6}$

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$\large \dfrac{a}{2} = x \\\\\\\large a = 2x$

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$\large \dfrac{b}{4} = x \\\\\\\large b = 4x$

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$\large \dfrac{c}{6} = x \\\\\\\large c = 6x$

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Substituindo os valores de a, b e c na expressão:

$\large a + b + c = 99 \\\\\\\large 2x + 4x + 6x = 99 \\\\\\\large 12x = 99 \\\\\\\large x = \dfrac{99}{12} \\\\\\\large x = 8,5$

Substituindo o valor de x em a, b e c

$\large a = 2x \\\\\large a = 2 ~. ~8,5 \\\\\large a =16,5$

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$\large b = 4x \\\\\large b = 4 ~. ~8,5 \\\\\large b =33$

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$\large c = 6x \\\\\large c = 6 ~. ~8,5 \\\\\large c =49,5$

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Prova:

16,5 + 33 + 49,5  = 99

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