1. **State the problem:** Solve the equation $$\frac{30}{90} = \frac{3x}{50}$$ for $x$. 2. **Use the cross-multiplication formula:** For two fractions equal to each other, $$\frac{a}{b} = \frac{c}{d}$$, the cross products are equal: $$a \times d = b \times c$$. 3. **Apply cross multiplication:** $$30 \times 50 = 90 \times 3x$$ 4. **Calculate the products:** $$1500 = 270x$$ 5. **Isolate $x$ by dividing both sides by 270:** $$x = \frac{1500}{270}$$ 6. **Simplify the fraction:** $$x = \frac{\cancel{1500}}{\cancel{270}} = \frac{1500 \div 30}{270 \div 30} = \frac{50}{9}$$ 7. **Final answer:** $$x = \frac{50}{9}$$