What approximate value should come in the place of (?) mark :
`?^(3) + (24.01)^(2) = (25.01)^(2) + 29.99% "of 49.99"`

Options

A. 2
B. 6
C. 3
D. 4

Answer

To solve the equation \( ?^3 + (24.01)^2 = (25.01)^2 + 29.99\% \text{ of } 49.99 \), we will approximate the values and simplify step by step.

### Step 1: Approximate the values
- Approximate \( 24.01 \) as \( 24 \)
- Approximate \( 25.01 \) as \( 25 \)
- Approximate \( 29.99\% \) as \( 30\% \)
- Approximate \( 49.99 \) as \( 50 \)

### Step 2: Rewrite the equation with approximations
The equation becomes:
\[ ?^3 + (24)^2 = (25)^2 + 30\% \text{ of } 50 \]

### Step 3: Calculate the squares
- \( (24)^2 = 576 \)
- \( (25)^2 = 625 \)
- \( 30\% \text{ of } 50 = \frac{30}{100} \times 50 = 15 \)

### Step 4: Substitute the calculated values back into the equation
Now the equation looks like:
\[ ?^3 + 576 = 625 + 15 \]

### Step 5: Simplify the right side
Calculate the right side:
\[ 625 + 15 = 640 \]

### Step 6: Set up the equation for \( ?^3 \)
Now we have:
\[ ?^3 + 576 = 640 \]

### Step 7: Isolate \( ?^3 \)
Subtract \( 576 \) from both sides:
\[ ?^3 = 640 - 576 \]
\[ ?^3 = 64 \]

### Step 8: Find the value of \( ? \)
To find \( ? \), take the cube root of \( 64 \):
\[ ? = \sqrt[3]{64} = 4 \]

Thus, the approximate value that should come in place of the question mark is \( 4 \).

### Final Answer
The value of \( ? \) is \( 4 \).

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