Question

2. Ştiind că 2a/3b =1/5, calculaţi 3a+2b/3a+b​

Answer 1

Răspuns:

$\frac{2a}{3b} =\frac{1}{5} = > 3b=2a*5= > 3b=10a= > a=\frac{3b}{10} \\\\\frac{3a+2b}{3a+b} =\frac{3\frac{3b}{10}+2b }{3\frac{3b}{10} +b} =\frac{\frac{29b}{10} }{\frac{19b}{10} } =\frac{29b}{10} *\frac{10}{19b} =\frac{29b}{19b} =\frac{29}{19}$

Answer 2

$\it \dfrac{2a}{3b}=\dfrac{1}{5} \Rightarrow \dfrac{2}{3}\cdot\dfrac{a}{b}=\dfrac{1}{5} \Rightarrow \dfrac{a}{b}=\dfrac{1}{5}\cdot\dfrac{3}{2} \Rightarrow\dfrac{a}{b}=\dfrac{3}{10} \Rightarrow \dfrac{a}{b}=0,3 \Rightarrow\\ \\ \\ \Rightarrow a=0,3b\bigg|_{\cdot3} \Rightarrow 3a=0,9b\ \ \ \ \ (*)\\ \\ \\ \dfrac{3a+2b}{3a+b}\ \stackrel{(*)}{=}\ \dfrac{0,9b+2b}{0,9b+b}=\dfrac{2,9b}{1,9b}=\dfrac{^{10)}2,9}{\ \ 1,9}=\dfrac{29}{19}$