Question

If $a:b=3:8$, Find the value of $\frac{4a+3b}{6a-b}$

Answer 1

Find the value of $\frac{4a+3b}{6a-b}$

Given: $a:b=3:8$
$\Rightarrow \frac{a}{b}=\frac{3}{8}\dots \text{equation}\left[1\right]$
We have $\frac{4a+3b}{6a-b}$
Divide numerator and denominator both by $b$ we get
$\frac{4a+3b}{6a-b}=\frac{4\times \left(\frac{a}{b}\right)+3}{6\times \left(\frac{a}{b}\right)-1}$
$=\frac{4\times \left(\frac{3}{8}\right)+3}{6\times \left(\frac{3}{8}\right)-1}$ [From$\left[1\right]$]
$=\frac{\frac{12+24}{8}}{\frac{18-8}{8}}$
$=\frac{12+24}{18-8}$
$=\frac{36}{10}$
$=\frac{18}{5}$

Hence the value of $\frac{4a+3b}{6a-b}$ is $\frac{18}{5}$.