If `(100 sqrt(25))/(sqrt(25) + x) = 50` then the value of x is :

Options

A. `25`
B. `1/(sqrt(25))`
C. `sqrt(25)`
D. `1/25`

Answer

To solve the equation \(\frac{100 \sqrt{25}}{\sqrt{25} + x} = 50\), we will follow these steps:

### Step 1: Simplify \(\sqrt{25}\)
First, we simplify \(\sqrt{25}\):
\[ \sqrt{25} = 5 \]

### Step 2: Substitute \(\sqrt{25}\) in the equation
Now, we substitute \(\sqrt{25}\) with 5 in the equation:
\[ \frac{100 \cdot 5}{5 + x} = 50 \]

### Step 3: Simplify the left side
Calculating \(100 \cdot 5\):
\[ \frac{500}{5 + x} = 50 \]

### Step 4: Cross-multiply
Next, we cross-multiply to eliminate the fraction:
\[ 500 = 50(5 + x) \]

### Step 5: Distribute on the right side
Distributing \(50\) on the right side:
\[ 500 = 250 + 50x \]

### Step 6: Isolate the term with \(x\)
Now, we isolate \(50x\) by subtracting \(250\) from both sides:
\[ 500 - 250 = 50x \]
\[ 250 = 50x \]

### Step 7: Solve for \(x\)
Finally, divide both sides by \(50\) to solve for \(x\):
\[ x = \frac{250}{50} \]
\[ x = 5 \]

### Final Answer
The value of \(x\) is \(5\).

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