1. Stating the problem: Find the unknown percentage $x$ such that $$65\% \text{ of } 180 + x\% \text{ of } 210 = 80\% \text{ of } 225.$$\n\n2. Write the equation using decimals for percentages:\n$$0.65 \times 180 + \frac{x}{100} \times 210 = 0.80 \times 225.$$\n\n3. Calculate the known products:\n$$0.65 \times 180 = 117,$$\n$$0.80 \times 225 = 180.$$\n\n4. Substitute these values back into the equation:\n$$117 + \frac{210x}{100} = 180.$$\n\n5. Simplify the equation:\n$$117 + 2.1x = 180.$$\n\n6. Isolate $x$:\n$$2.1x = 180 - 117 = 63,$$\n$$x = \frac{63}{2.1} = 30.$$\n\n7. Conclusion: The unknown percentage is $30\%$.\n\nAnswer: (b) 30