`133.99sqrt(?)+42.0032sqrt(?)=(176)/(12.998)xx(?)`

Options

A. 81
B. 72
C. 169
D. 121

Explanation

To solve the equation \( 133.99\sqrt{x} + 42.0032\sqrt{x} = \frac{176}{12.998} \times x \), we will follow these steps:

### Step 1: Simplify the Equation
Combine the terms on the left side of the equation:
\[ (133.99 + 42.0032)\sqrt{x} = \frac{176}{12.998} \times x \]
Calculating \( 133.99 + 42.0032 \):
\[ 175.9932\sqrt{x} = \frac{176}{12.998} \times x \]

### Step 2: Approximate the Constants
Since we are looking for an approximate solution, we can round the numbers:
- \( 175.9932 \) is approximately \( 176 \)
- \( 12.998 \) is approximately \( 13 \)

Thus, we can rewrite the equation as:
\[ 176\sqrt{x} \approx \frac{176}{13} \times x \]

### Step 3: Cancel Out Common Terms
We can divide both sides of the equation by \( 176 \) (assuming \( 176 \neq 0 \)):
\[ \sqrt{x} \approx \frac{x}{13} \]

### Step 4: Rearranging the Equation
Multiply both sides by \( 13 \):
\[ 13\sqrt{x} \approx x \]

### Step 5: Isolate \( \sqrt{x} \)
Rearranging gives us:
\[ \frac{x}{\sqrt{x}} \approx 13 \]
This simplifies to:
\[ \sqrt{x} \approx 13 \]

### Step 6: Square Both Sides
To find \( x \), square both sides:
\[ x \approx 13^2 \]
Calculating \( 13^2 \):
\[ x \approx 169 \]

### Final Answer
Thus, the approximate value of \( x \) is:
\[ \boxed{169} \]