Question

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

Answer 1

Using Componendo and Dividendo on $$\frac{3x + 5y}{3x - 5y} = \frac{7}{3}$$, we get:

$$\frac{(3x + 5y) + (3x - 5y)}{(3x + 5y) - (3x - 5y)} = \frac{7 + 3}{7 - 3}$$

Simplify both sides:

$$\frac{6x}{10y} = \frac{10}{4}$$ 

$$\frac{3x}{5y} = \frac{5}{2}$$

Multiply both sides by $$\frac{5}{3}$$:

$$\frac{x}{y} = \frac{5 \times 5}{2 \times 3} = \frac{25}{6}$$

Therefore, $$x : y = 25 : 6$$.