What approximate value should come in the place of questions (?) mark.
?% of 249.95 + `(3.99)^(3) = (6.01)^(3) - root(4)(16.01)`

Options

A. 60
B. 40
C. 48
D. 80

Answer

To solve the equation step by step, we need to simplify and approximate the values given in the question.

### Step 1: Rewrite the equation with approximations
The original equation is:
\[ ? \% \text{ of } 249.95 + (3.99)^3 = (6.01)^3 - \sqrt[4]{16.01} \]
We can approximate the values:
- \(249.95 \approx 250\)
- \(3.99 \approx 4\)
- \(6.01 \approx 6\)
- \(\sqrt[4]{16.01} \approx \sqrt[4]{16} = 2\)

So, we rewrite the equation as:
\[ ? \% \text{ of } 250 + 4^3 = 6^3 - 2 \]

### Step 2: Calculate the cubes
Now we calculate the cubes:
- \(4^3 = 64\)
- \(6^3 = 216\)

Substituting these values into the equation gives:
\[ ? \% \text{ of } 250 + 64 = 216 - 2 \]

### Step 3: Simplify the right-hand side
Now simplify the right-hand side:
\[ 216 - 2 = 214 \]
So the equation now looks like:
\[ ? \% \text{ of } 250 + 64 = 214 \]

### Step 4: Isolate the percentage term
Now, we isolate the percentage term:
\[ ? \% \text{ of } 250 = 214 - 64 \]
Calculating the right side:
\[ 214 - 64 = 150 \]
So we have:
\[ ? \% \text{ of } 250 = 150 \]

### Step 5: Convert percentage to decimal
Recall that \(? \% \text{ of } 250\) can be expressed as:
\[ \frac{?}{100} \times 250 = 150 \]

### Step 6: Solve for ?
Now, we can solve for \(?\):
\[ \frac{?}{100} \times 250 = 150 \]
Multiplying both sides by 100:
\[ ? \times 250 = 15000 \]
Now, divide both sides by 250:
\[ ? = \frac{15000}{250} = 60 \]

### Conclusion
The approximate value that should come in place of the question mark is:
\[ \boxed{60} \]