Question

If $A:B=3:4$ and $B:C=6:7$, find:
$\left(i\right)$ $A:B:C$
$\left(ii\right)$ $A:C$

Answer 1

$A:B=3:4\Rightarrow \frac{A}{B}=\frac{3}{4}\Rightarrow \frac{A}{3}=\frac{B}{4}\Rightarrow \frac{A}{9}=\frac{B}{12}$

And $B:C=6:7\Rightarrow \frac{B}{C}=\frac{6}{7}\Rightarrow \frac{B}{6}=\frac{C}{7}\Rightarrow \frac{B}{12}=\frac{C}{14}$

$\Rightarrow \frac{A}{9}=\frac{B}{12}=\frac{C}{14}\left(i\right)\therefore A:B:C=9:12:14\left(ii\right)also\frac{A}{9}=\frac{C}{14}\Rightarrow \frac{A}{C}=\frac{9}{14}\Rightarrow A:C=9:14$