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1. If m : n = 3 : 2, then (4m + 5n) : (4m - 5n) is equal to = ?

A. 4 : 9

B. 9 : 4

C. 11 : 1

D. 9 : 1

Solution:

\begin{aligned} m : n = 3 : 2 \\ \frac{m}{n} = \frac{3}{2} \\ \Rightarrow \frac{4 m + 5 n}{4 m - 5 n} \\ \Rightarrow \frac{n (4 \frac{m}{n} + 5)}{n (4 \frac{m}{n} - 5)} \\ \Rightarrow \frac{4 \times \frac{3}{2} + 5}{4 \times \frac{3}{2} - 5} \\ \Rightarrow \frac{6 + 5}{6 - 5} \\ \Rightarrow \frac{11}{1} \\ \Rightarrow 11 : 1 \end{aligned}

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