Question

If $a:b=3:5$ find $(3a+5b):(7a-2b).$

Answer 1

$\frac{a}{b}=\frac{3}{5}$

$\Rightarrow a=\frac{3b}{5}$

$3a+5b:7a-2b$

$3\times \frac{3b}{5}+5b:7\times \frac{3b}{5}-2b$

$\frac{\frac{9b}{5}+5b}{\frac{21b}{5}-2b}=\frac{9b+25b}{21b-10b}$

$=\frac{34b}{11b}=34:11$.