Find the approximate value of (?) in the following questions.
`(1695.94)/(?% "of 799.9") + sqrt(1023.98) = 58.47`

Options

A. 30
B. 8
C. 48
D. 76

Answer

To solve the equation \( \frac{1695.94}{(?\% \text{ of } 799.9)} + \sqrt{1023.98} = 58.47 \), we will follow these steps:

### Step 1: Approximate the values
We will approximate the numbers in the equation:
- \( 1695.94 \approx 1696 \)
- \( 799.9 \approx 800 \)
- \( 1023.98 \approx 1024 \)
- \( 58.47 \approx 58.47 \) (we will keep this as is for now)

So, the equation becomes:
\[ \frac{1696}{(?\% \text{ of } 800)} + \sqrt{1024} = 58.47 \]

### Step 2: Calculate the square root
Next, we calculate \( \sqrt{1024} \):
\[ \sqrt{1024} = 32 \]

Now, substitute this value back into the equation:
\[ \frac{1696}{(?\% \text{ of } 800)} + 32 = 58.47 \]

### Step 3: Isolate the fraction
Subtract \( 32 \) from both sides:
\[ \frac{1696}{(?\% \text{ of } 800)} = 58.47 - 32 \]
\[ \frac{1696}{(?\% \text{ of } 800)} = 26.47 \]

### Step 4: Express percentage as a fraction
Recall that \( ?\% \text{ of } 800 = \frac{?}{100} \times 800 \). Thus, we can rewrite the equation:
\[ \frac{1696}{\frac{?}{100} \times 800} = 26.47 \]

### Step 5: Simplify the equation
Multiply both sides by \( \frac{?}{100} \times 800 \):
\[ 1696 = 26.47 \times \frac{?}{100} \times 800 \]

### Step 6: Solve for ?
Now, simplify the right side:
\[ 1696 = \frac{26.47 \times 800}{100} \times ? \]
\[ 1696 = 0.2647 \times 800 \times ? \]
\[ 1696 = 211.76 \times ? \]

### Step 7: Isolate ?
Now, divide both sides by \( 211.76 \):
\[ ? = \frac{1696}{211.76} \]
Calculating this gives:
\[ ? \approx 8.01 \]

### Step 8: Approximate the answer
Since we need the approximate value, we round \( 8.01 \) to \( 8 \).

Thus, the approximate value of \( ? \) is:
\[ \boxed{8} \]