Question
If $\frac{a}{b}=\frac{7}{4}$ then find the ratio $\frac{5 a-b}{b}$.
✓
Answer
$\quad \frac{a}{b}=\frac{7}{4}$
$
\therefore \quad \frac{a}{7}=\frac{b}{4} \quad \ldots \text { (using alternando) }
$
Let $\frac{a}{7}=\frac{b}{4}=m$
$
\begin{aligned}
\therefore a & =7 m, \quad b=4 m \\
\therefore \frac{5 a-b}{b} & =\frac{5(7 m)-4 m}{4 m} \\
& =\frac{35 m-4 m}{4 m} \\
& =\frac{31}{4}
\end{aligned}
$
$
\therefore \quad \frac{a}{7}=\frac{b}{4} \quad \ldots \text { (using alternando) }
$
Let $\frac{a}{7}=\frac{b}{4}=m$
$
\begin{aligned}
\therefore a & =7 m, \quad b=4 m \\
\therefore \frac{5 a-b}{b} & =\frac{5(7 m)-4 m}{4 m} \\
& =\frac{35 m-4 m}{4 m} \\
& =\frac{31}{4}
\end{aligned}
$
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