Question

If $a:b=4:7$, find the following:

(iii) $\frac{5a-4b}{2a-3b}$

Answer 1

Given: $\frac{a}{b}=\frac{4}{7}$

$\Rightarrow \frac{5a-4b}{2a-3b}$

Divide both numerator and denominator by $b$,

$=\frac{5\left(\frac{a}{b}\right)-4}{2\left(\frac{a}{b}\right)-3}$

On substituting the value $\frac{a}{b}=\frac{4}{7}$,

$=\frac{5\left(\frac{4}{7}\right)-4}{2\left(\frac{4}{7}\right)-3}$

$=\frac{5\times 4-4\times 7}{2\times 4-3\times 7}$

$=\frac{20-28}{8-21}$

$=\frac{-8}{-13}$

$=\frac{8}{13}$

Hence, the value of $\frac{5a-4b}{2a-3b}\text{is}\frac{8}{13}$.