Question

2a+3b/a+7b=5/6
Aflati raportul dintre a si b

Answer 1

 

$\displaystyle\bf\\\frac{2a+3b^\b{(b}}{a+7b}=\frac{5}{6}\\\\\textbf{Fractia din stanga egalului o simplificam fortat cu b.}\\\\\frac{~~\dfrac{2a+3b}{b}~~}{\dfrac{a+7b}{b}}=\frac{5}{6}\\\\\\\frac{~~\dfrac{2a}{b}+\dfrac{3b}{b}~~}{~~\dfrac{a}{b}+\dfrac{7b}{b}~~}=\frac{5}{6}\\\\\\\frac{~~2\times\dfrac{a}{b}+3~~}{~~\dfrac{a}{b}+7~~}=\frac{5}{6}$

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$\displaystyle\bf\\Produsul~mezilor~=~produsul~extremilor\\\\6\left(2\times\frac{a}{b}+3\right)=5\left(\frac{a}{b}+7\right)\\\\\\12\times\frac{a}{b}+18=5\times\frac{a}{b}+35\\\\\\12\times\frac{a}{b}-5\times\frac{a}{b}=35-18\\\\\\7\times\frac{a}{b}=17\\\\\\\boxed{\bf\frac{a}{b}=\frac{17}{7}}$