Question

If $$x : y = 3 : 2$$, find $$(5x - 3y) : (7x + 2y)$$.

Answer 1

Let $$x = 3k$$ and $$y = 2k$$.

Substitute these into the expression: $$\frac{5x - 3y}{7x + 2y} = \frac{5(3k) - 3(2k)}{7(3k) + 2(2k)}$$

Simplify: $$\frac{15k - 6k}{21k + 4k} = \frac{9k}{25k} = \frac{9}{25}$$

Therefore, $$(5x - 3y) : (7x + 2y) = 9 : 25$$.