The sum of two numbers is equal to the sum of the square of 11 and the cube of 9. The larger number is 25 less than the square of 25. What is the sum of twice 30\% of the smaller number and half of the larger number?

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**Solution:**

1. Calculate the sum of the square of 11 and the cube of 9:
   - Square of 11: $11^2 = 121$
   - Cube of 9: $9^3 = 729$
   - Sum: $121 + 729 = 850$

2. Let the two numbers be *x* (smaller) and *y* (larger). Given:
   $$x + y = 850$$

3. The larger number *y* is 25 less than the square of 25:
   $$y = 25^2 - 25 = 625 - 25 = 600$$

4. Find the smaller number *x*:
   $$x = 850 - 600 = 250$$

5. Calculate twice 30\% of the smaller number:
   - 30\% of *x* = $0.3 	imes 250 = 75$
   - Twice of this = $2 	imes 75 = 150$

6. Calculate half of the larger number:
   $$\frac{600}{2} = 300$$

7. Find the required sum:
   $$150 + 300 = 450$$

**Answer:** 450

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