If a : b = 3 : 5, find (3a + 5b): (7a – 2b). - Vidyadip

Question

If a : b = 3 : 5, find (3a + 5b): (7a – 2b).

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Answer

$
\begin{aligned}
& a: b=3: 5 \\
& \Rightarrow \frac{a}{b}=\frac{3}{5} \\
& \Rightarrow 3 a+5 n: 7 a-2 b
\end{aligned}$
Dividing each term by $b$
$
\begin{aligned}
& 3 \frac{a}{b}+5: 3 \frac{a}{b}-2 \\
& \Rightarrow 3 \times \frac{3}{5}+5: 7 \times \frac{3}{5}-2 \\
& \Rightarrow\left(\frac{9}{5}+5\right):\left(\frac{21}{5}-2\right) \\
& \Rightarrow \frac{9+25}{5}: \frac{21-10}{5} \\
& \Rightarrow \frac{34}{5}: \frac{11}{5} \\
& =34: 11 .
\end{aligned}
$

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