Directions (36 -40):What approximate value should come in the place of question (?) mark.

? % of 750.03 + ${\left(14.99\right)}^2$ = ${\left(8.03\right)}^2$ + 356.01

The correct option is 26.

To solve this approximation problem, let us round off each number to its nearest integer value:

• 750.03 ≈ 750

• 14.99 ≈ 15

• 8.03 ≈ 8

• 356.01 ≈ 356

Let the unknown value in place of the question mark (?) be $x$.

Now, substitute the rounded values into the given equation:

$(\frac{x}{100}\times 750)+{\left(15\right)}^2={\left(8\right)}^2+356$

Step 1: Calculate the squares of the numbers.

${\left(15\right)}^2=225$

${\left(8\right)}^2=64$

Step 2: Substitute these square values back into the equation.

$(7.5\times x)+225=64+356$

Step 3: Simplify the right side of the equation.

$64+356=420$

$7.5\times x+225=420$

Step 4: Subtract 225 from both sides to isolate the term containing $x$.

$7.5\times x=420-225$

$7.5\times x=195$

Step 5: Solve for $x$.

$x=\frac{195}{7.5}$

$x=\frac{1950}{75}=26$

Therefore, the approximate value that should come in place of the question mark (?) is 26.