What approximate value should come in the place of (?) mark :
`(128.05)/(?) + (17.01)^(2) = 19.99% "of" 1525.01`

Options

A. 6
B. 12
C. 4
D. 8

Answer

To solve the equation \( \frac{128.05}{?} + (17.01)^2 = 19.99\% \text{ of } 1525.01 \), we will follow these steps:

### Step 1: Calculate \( 19.99\% \text{ of } 1525.01 \)
First, we need to find \( 19.99\% \) of \( 1525.01 \).

\[ 19.99\% = \frac{19.99}{100} = 0.1999 \]

Now, calculate:

\[ 0.1999 \times 1525.01 \approx 304.85 \]

### Step 2: Simplify the equation
Now we can rewrite the equation:

\[ \frac{128.05}{?} + (17.01)^2 = 304.85 \]

### Step 3: Calculate \( (17.01)^2 \)
Next, we calculate \( (17.01)^2 \):

\[ (17.01)^2 \approx 289.34 \]

### Step 4: Substitute and solve for \( ? \)
Now substitute \( (17.01)^2 \) back into the equation:

\[ \frac{128.05}{?} + 289.34 = 304.85 \]

Now, isolate \( \frac{128.05}{?} \):

\[ \frac{128.05}{?} = 304.85 - 289.34 \]

Calculating the right side:

\[ \frac{128.05}{?} \approx 15.51 \]

### Step 5: Solve for \( ? \)
Now, we can solve for \( ? \):

\[ ? = \frac{128.05}{15.51} \]

Calculating this gives:

\[ ? \approx 8.25 \]

### Step 6: Approximate to the nearest option
The closest approximate value from the given options (6, 12, 4, 6) is 6.

### Final Answer
Thus, the approximate value that should come in place of the (?) mark is **6**.

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