Question

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

(i) $\frac{5a+2b}{5a-2b}$

Answer 1

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

$\frac{5a+2b}{5a-2b}$

Divide both numerator and denominator by $b$,

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

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

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

$=\frac{20+2\times 7}{20-2\times 7}$

$=\frac{20+14}{20-14}$

$=\frac{34}{6}$

$=\frac{17}{3}$ (On dividing each term by $2$)

Hence, the value of $\frac{5a+2b}{5a-2b}\text{is}\frac{17}{3}$.