Directions: What approximate value will come in place of the question mark (?) in the following equation? (You are not expected to calculate the exact value.)

24.97% of 640.18 - 54.91% of 960.24 = 416.12 - ?²

The correct answer is 28.

We are required to find the approximate value of the question mark (?) in the given equation:

$24.97\%\text{of}640.18-54.91\%\text{of}960.24=416.12-{?}^2$

Step 1: Round off the given numbers to their nearest manageable values.

24.97% can be rounded off to 25%.

640.18 can be rounded off to 640.

54.91% can be rounded off to 55%.

960.24 can be rounded off to 960.

416.12 can be rounded off to 416.

Step 2: Simplify the approximated values on the left-hand side.

First, calculate 25% of 640:

$25\%\text{of}640=\frac{1}{4}\times 640=160$

Next, calculate 55% of 960:

$55\%\text{of}960=\frac{55}{100}\times 960=0.55\times 960=528$

Now, subtract the second result from the first:

$160-528=-368$

Step 3: Substitute the calculated value into the equation and solve for ?.

$-368=416-{?}^2$

Rearrange the terms to isolate ${?}^2$:

${?}^2=416+368$

${?}^2=784$

Taking the square root on both sides:

$?=\sqrt{784}=28$

Hence, the approximate value that will come in place of the question mark is 28.