Find the approximate value that should come in place of the question mark (?) in the following equation:

$(?+461.19)+150.08\%\text{of}\left(\frac{5999.92}{299.98}\right)=29.89\times 34.92$

The correct answer is 559.

Given equation:

$(?+461.19)+150.08\%\text{of}\left(\frac{5999.92}{299.98}\right)=29.89\times 34.92$

Approximating the terms in the equation to their nearest whole numbers:
461.19 ≈ 461
150.08% ≈ 150%
5999.92 ≈ 6000
299.98 ≈ 300
29.89 ≈ 30
34.92 ≈ 35

Substitute these approximate values into the equation:

$(?+461)+150\%\text{of}\left(\frac{6000}{300}\right)=30\times 35$

First, simplify the fraction inside the bracket:

$\frac{6000}{300}=20$

Next, calculate 150% of 20:

$150\%\text{of}20=\frac{150}{100}\times 20=1.5\times 20=30$

Now, calculate the right-hand side of the equation:

$30\times 35=1050$

Substitute all the calculated values back into the simplified equation:

$(?+461)+30=1050$

Simplify the left-hand side:

$?+491=1050$

Solve for the missing value (?):

$?=1050-491$

$?=559$

Hence, the approximate value that should come in place of the question mark is 559.