Question

If a: b = 4: 7, find the following: 

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

Answer 1

a : b = 4 : 7 ⇒ ${\displaystyle \frac{\text{a}}{\text{b}}=\frac{4}{7}}$

${\displaystyle \frac{5\text{a}+2\text{b}}{5\text{a}-2\text{b}}=\frac{5\frac{\text{a}}{\text{b}}+2}{5\frac{\text{a}}{\text{b}}-2}}$

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

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

= ${\displaystyle \frac{34}{6}}$

= ${\displaystyle \frac{17}{3}}$