If a: b=4: 7, find the following: 5 a-4 b 2 a-3 b - Vidyadip

Question

If $a: b=4: 7$, find the following:
$\frac{5 a-4 b}{2 a-3 b}$

✓

Answer

$a: b=4: 7 \Rightarrow \frac{a}{b}=\frac{4}{7} $
$ \frac{5 a-4 b}{2 a-3 b}=\frac{5 \times \frac{a}{b}-4}{2 \times \frac{a}{b}-3} $
$ =\frac{5 \times \frac{4}{7}-4}{2 \times \frac{4}{7}-3} $
$=\frac{\frac{20}{7}-4}{\frac{8}{7}-3} $
$ =\frac{-8}{-13}=\frac{8}{13}$

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