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Area of Rectangle

If x/y = 2m...

Question

If $\frac{x}{y} = \frac{2 m - 3}{2 - 3 m}$ , express m in terms of x and y.
Find the value of m correct to two significant figures, if $2 x = y = 10$ .

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Solution

Given, $\frac{x}{y} = \frac{2 m - 3}{2 - 3 m}$
$=> 2 x - 3 m x = 2 m y - 3 y$
$=> 2 x + 3 y = 2 m y + 3 m x$
$=> 2 x + 3 y = m (2 y + 3 x)$
$=> m = \frac{2 x + 3 y}{3 x + 2 y}$
When, $y = 10;$ and $2 x = 10 => x = 5$ , we get
$m = \frac{10 + 30}{15 + 20} = \frac{40}{35} = 1.1$

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