`34.02% "of " 550.09div?=594.05divsqrt(2916.03)`

Options

A. 14
B. 21
C. 8
D. 17

Explanation

To solve the problem step by step, we need to find the value of the question mark (K) in the equation:

\[ 34.02\% \text{ of } 550.09 \div K = \frac{594.05}{\sqrt{2916.03}} \]

### Step 1: Approximate the percentages and numbers
First, we can approximate the values to make calculations easier:
- \( 34.02\% \) can be approximated to \( 34\% \).
- \( 550.09 \) can be approximated to \( 550 \).
- \( 594.05 \) can be approximated to \( 594 \).
- \( \sqrt{2916.03} \) can be approximated to \( \sqrt{2916} \).

### Step 2: Convert percentage to decimal
Convert \( 34\% \) to decimal:
\[ 34\% = \frac{34}{100} = 0.34 \]

### Step 3: Set up the equation
Now, we can rewrite the equation using the approximated values:
\[ 0.34 \times 550 \div K = \frac{594}{\sqrt{2916}} \]

### Step 4: Calculate the square root
Calculate \( \sqrt{2916} \):
\[ \sqrt{2916} = 54 \quad (\text{since } 54 \times 54 = 2916) \]

### Step 5: Substitute back into the equation
Now substitute back into the equation:
\[ 0.34 \times 550 \div K = \frac{594}{54} \]

### Step 6: Calculate the right-hand side
Calculate \( \frac{594}{54} \):
\[ \frac{594}{54} = 11 \]

### Step 7: Calculate the left-hand side
Calculate \( 0.34 \times 550 \):
\[ 0.34 \times 550 = 187 \]

### Step 8: Set up the final equation
Now we have:
\[ \frac{187}{K} = 11 \]

### Step 9: Solve for K
To find \( K \), we can cross-multiply:
\[ 187 = 11K \]
Now divide both sides by 11:
\[ K = \frac{187}{11} \approx 17 \]

### Step 10: Conclusion
Thus, the value of the question mark \( K \) is approximately \( 17 \).