waecmaths question:
If $x:y=\tfrac{1}{4}:\tfrac{3}{8}$and $y:z=\tfrac{1}{3}:\tfrac{4}{9}$, find x : z
Option A:
2: 3
Option B:
3:4
Option C:
3:8
Option D:
1:2
waecmaths solution:
$\begin{align} & \frac{x}{y}=\frac{\tfrac{1}{4}}{\tfrac{3}{8}}\Leftrightarrow \text{ }\frac{x}{y}=\frac{1}{4}\times \frac{8}{3}=\frac{2}{3} \\ & y=\frac{3x}{2}---(i) \\ & \frac{y}{z}=\frac{\tfrac{1}{3}}{\tfrac{4}{9}}\Leftrightarrow \frac{y}{z}=\frac{1}{3}\times \frac{9}{4}=\frac{3}{4} \\ & y=\frac{3}{4}z---(ii) \\ & \text{Equating (i) and (ii)} \\ & \frac{3x}{2}=\frac{3z}{4}\Leftrightarrow \frac{x}{z}=\frac{2}{4}=\frac{1}{2} \\ & x:z=1:2 \\\end{align}$
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