Two values together equal the sum of the square of 20 and the cube of 8. The greater value is 8 less than the square of 30. What is the total of 20% of the smaller value and one-half of the greater value?

The correct answer is 450.

Step 1: Find the total sum of the two values.
The problem states that two values together equal the sum of the square of 20 and the cube of 8.

$\text{Square of 20}={20}^2=400$

$\text{Cube of 8}=8^3=512$

$\text{Total sum of the two values}=400+512=912$

Step 2: Determine the greater value.
The greater value is 8 less than the square of 30.

$\text{Square of 30}={30}^2=900$

$\text{Greater value}=900-8=892$

Step 3: Calculate the smaller value.
Subtract the greater value from the total sum of the two values.

$\text{Smaller value}=912-892=20$

Step 4: Calculate 20% of the smaller value and one-half of the greater value.

$20\%\text{of the smaller value}=\frac{20}{100}\times 20=4$

$\text{One-half of the greater value}=\frac{1}{2}\times 892=446$

Step 5: Find the required total.

$\text{Total}=4+446=450$

Thus, the total of 20% of the smaller value and one-half of the greater value is 450.