Question

If $\frac{5a+2b}{5a-2b}=\frac{5}{3}$, then find the value of a : b. [2 Marks]

Answer 1

$\frac{5a+2b}{5a-2b}=\frac{5}{3}$

$\frac{5a+2b+5a-2b}{5a+2b-5a+2b}=\frac{5+3}{5-3}$ [Applying componendo and dividendo] [1 Mark]

$\frac{10a}{4b}=\frac{8}{2}$

$\frac{2\left(5a\right)}{2\left(2b\right)}=\frac{8}{2}$

$\frac{a}{b}=\frac{8}{5}$

a : b = 8 : 5 [1 Mark]