Răspuns:
Explicație pas cu pas:
{a ; b ; c} d.p {0,26 ; 0,1(6) ; 0,(09)}
[tex] \frac{a}{0,25} = \frac{b}{0,1(6)} = \frac{c}{0,(09)} = k, \\ [/tex] unde k = coeficient de propoționalitate
[tex]0.25 = \frac{25 {}^{(25} }{100} = \frac{1}{4} \\ [/tex]
[tex]0,1(6) = \frac{16 - 1}{90} = \frac{15 {}^{(15} }{90} = \frac{1}{6} \\ [/tex]
[tex]0,(09) = \frac{9 {}^{(9} }{99} = \frac{1}{11} \\ [/tex]
[tex] \frac{a}{ \frac{1}{4} } = \frac{b}{ \frac{1}{6} } = \frac{c}{ \frac{1}{11} } = k \\ [/tex]
[tex]a = \frac{1}{4} k \\ [/tex]
[tex]b = \frac{1}{6} k \\ [/tex]
[tex]c = \frac{1}{11} k \\ [/tex]
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8a + 4b - 3c = 52
[tex]8 \times \frac{1}{4} k + 4 \times \frac{1}{6} k - 3 \times \frac{1}{11} k = 52 \\ [/tex]
[tex] \frac{8}{ 4} k + \frac{4 {}^{(2} }{6} k - \frac{3}{11} k = 5 2\\ [/tex]
[tex]2k + \frac{2}{3} k - \frac{3}{11} k = 52 \: \: \: \Big| \times 33 \\ [/tex]
66k + 22k - 9k = 1716
79k = 1716
[tex]k = \frac{1716}{79} \\ [/tex]
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[tex]a = \frac{1}{4} \times \frac{1716}{79} = \frac{1716 {}^{(4} }{316} = \frac{429}{79} \\ [/tex]
[tex]b = \frac{1}{6} \times \frac{1719}{79} = \frac{1716 {}^{(6} }{474} = \frac{286}{79} \\ [/tex]
[tex]c = \frac{1}{11} \times \frac{1716}{79} = \frac{1716 {}^{(11} }{869} = \frac{156}{79} \\ [/tex]
