Determine the approximate value that should replace the question mark (?) in the mathematical expression below.

$\frac{87.01\times 7.98}{?}+7.99\%\text{of}1149.98={\left(}^{18.01}$

The correct option is 3.

To find the approximate value of the question mark (?), let us round off each value in the given mathematical expression to its nearest integer for simple calculation:

$87.01\approx 87$

$7.98\approx 8$

$7.99\%\approx 8\%$

$1149.98\approx 1150$

$18.01\approx 18$

Let the missing value (?) be represented by x. Substituting the rounded values into the expression gives:

$\frac{87\times 8}{x}+8\%\text{of}1150={18}^2$

Now, calculate each component step-by-step:

1. Product of the numerator: 87 × 8 = 696

2. Percentage component: 8% of 1150 = (8 / 100) × 1150 = 92

3. Square component: 18² = 324

Substituting these calculated values back into the equation:

$\frac{696}{x}+92=324$

Subtract 92 from both sides of the equation:

$\frac{696}{x}=324-92$

$\frac{696}{x}=232$

Now, solve for x:

$x=\frac{696}{232}=3$

Therefore, the value that should replace the question mark (?) is 3.