What approximate value should come in the place of questions (?) mark.
32.01% of ? + `(17.99)^(2)` = 75.99% of 500.04

Options

A. 175
B. 150
C. 125
D. 225

Answer

To solve the equation step by step, we start with the given equation:

\[ 32.01\% \text{ of } ? + (17.99)^2 = 75.99\% \text{ of } 500.04 \]

### Step 1: Convert percentages to decimals
First, we convert the percentages to decimal form:
- \( 32.01\% = \frac{32.01}{100} = 0.3201 \)
- \( 75.99\% = \frac{75.99}{100} = 0.7599 \)

### Step 2: Calculate \( (17.99)^2 \)
Next, we calculate \( (17.99)^2 \):
- \( (17.99)^2 \approx 18^2 = 324 \) (using approximation for simplicity)

### Step 3: Calculate \( 75.99\% \text{ of } 500.04 \)
Now, we calculate \( 75.99\% \text{ of } 500.04 \):
- \( 0.7599 \times 500.04 \approx 0.76 \times 500 \approx 380 \)

### Step 4: Set up the equation
Now we can rewrite the equation with these approximations:
\[ 0.3201 \times ? + 324 \approx 380 \]

### Step 5: Isolate the variable
Next, we isolate the variable \( ? \):
\[ 0.3201 \times ? \approx 380 - 324 \]
\[ 0.3201 \times ? \approx 56 \]

### Step 6: Solve for \( ? \)
Now, we solve for \( ? \):
\[ ? \approx \frac{56}{0.3201} \]
Calculating this gives:
\[ ? \approx 175 \]

### Final Answer
Thus, the approximate value that should come in place of the question mark is:
\[ ? \approx 175 \]

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