What approximate value should come in the place of question (?) mark.
56.01% of ? + `(11.99)^(2) = 68.01%` of 499.99

Options

A. 250
B. 300
C. 150
D. 350

Answer

To solve the equation \( 56.01\% \text{ of } ? + (11.99)^2 = 68.01\% \text{ of } 499.99 \), we will follow these steps:

### Step 1: Approximate the percentages and numbers
We can round the percentages and the numbers to make calculations easier:
- \( 56.01\% \) can be approximated to \( 56\% \).
- \( 11.99 \) can be approximated to \( 12 \).
- \( 68.01\% \) can be approximated to \( 68\% \).
- \( 499.99 \) can be approximated to \( 500 \).

### Step 2: Rewrite the equation with approximations
Now we can rewrite the equation using these approximations:
\[ 56\% \text{ of } ? + 12^2 = 68\% \text{ of } 500 \]

### Step 3: Calculate \( 12^2 \)
Calculating \( 12^2 \):
\[ 12^2 = 144 \]

### Step 4: Calculate \( 68\% \text{ of } 500 \)
Calculating \( 68\% \text{ of } 500 \):
\[ 68\% \text{ of } 500 = \frac{68}{100} \times 500 = 340 \]

### Step 5: Substitute back into the equation
Now substitute the values back into the equation:
\[ 56\% \text{ of } ? + 144 = 340 \]

### Step 6: Isolate \( 56\% \text{ of } ? \)
To isolate \( 56\% \text{ of } ? \):
\[ 56\% \text{ of } ? = 340 - 144 \]
Calculating the right side:
\[ 340 - 144 = 196 \]

### Step 7: Solve for \( ? \)
Now we have:
\[ 56\% \text{ of } ? = 196 \]
This can be rewritten as:
\[ \frac{56}{100} \times ? = 196 \]
To solve for \( ? \):
\[ ? = \frac{196 \times 100}{56} \]

### Step 8: Calculate \( ? \)
Calculating \( ? \):
\[ ? = \frac{19600}{56} \approx 350 \]

### Final Answer
Thus, the approximate value that should come in place of the question mark is \( 350 \).

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