Question

Știind ca 2a/3b=1/5, calculati 3a+2b/3a+b​

Answer 1

Răspuns:

$\frac{3a + 2b}{3a + b} = \frac{29}{19}$

Explicație pas cu pas:

$\frac{2 a}{3b} = \frac{1}{5} \Rightarrow10a = 3b\Rightarrow a = \frac{3b}{10}$

$3a + 2b = 3 \times \frac{3b}{10} + 2b = \frac{9b}{10} + {}^{10)} 2b = \frac{9b}{10} + \frac{20b}{10} = \frac{29b}{10}$

$3a + b = 3 \times \frac{3b}{10} + b = \frac{9b}{10} + {}^{10)} b = \frac{9b}{10} + \frac{10b}{10} = \frac{19b}{10}$

$\frac{3a + 2b}{ 3a + b } = \frac{ \frac{29b}{10} }{ \frac{19b}{10} } = \frac{29 \not b}{ \not10} \times \frac{ \not10}{19 \not b} =\boxed{ \frac{29}{19}}$