Question

If $(3a+2b):(2a+5b)=12:19$, then find $a:b$.

Answer 1

$\frac{3a+2b}{2a+5b}=\frac{12}{19}$

$3a+2b=12...\left(1\right)$

$2a+5b=19...\left(2\right)$

multiply equation (1) by 2 and multiply equation (2) by 3

$6a+4b=24$

$6a+15b=57$

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__________________

$-11b=-33$

$b=3$

Subsituting $b=3$ in wquation (1)

$3a+2b=12$

$3a+6=12$

$3a=12-6$

$3a=6$

$a=2$

$\therefore a:b=2:3$ (or) $\frac{a}{b}=\frac{2}{3}$