5% of `420xx?%` of 150=252

Options

A. 12
B. 5
C. 6
D. 8

Explanation

To solve the equation \( 5\% \text{ of } 420 \times ?\% \text{ of } 150 = 252 \), we can follow these steps:

### Step 1: Convert percentages to fractions
We know that \( 5\% \) can be written as \( \frac{5}{100} \) and \( ?\% \) can be written as \( \frac{x}{100} \).

### Step 2: Rewrite the equation
The equation can be rewritten as:
\[ \frac{5}{100} \times 420 \times \frac{x}{100} \times 150 = 252 \]

### Step 3: Simplify the equation
First, simplify \( \frac{5}{100} \) to \( \frac{1}{20} \):
\[ \frac{1}{20} \times 420 \times \frac{x}{100} \times 150 = 252 \]

### Step 4: Calculate \( \frac{1}{20} \times 420 \)
Calculating \( \frac{1}{20} \times 420 \):
\[ \frac{420}{20} = 21 \]
So now the equation becomes:
\[ 21 \times \frac{x}{100} \times 150 = 252 \]

### Step 5: Calculate \( 21 \times 150 \)
Now calculate \( 21 \times 150 \):
\[ 21 \times 150 = 3150 \]
Thus, the equation simplifies to:
\[ \frac{3150x}{100} = 252 \]

### Step 6: Eliminate the fraction
Multiply both sides by 100 to eliminate the fraction:
\[ 3150x = 25200 \]

### Step 7: Solve for \( x \)
Now, divide both sides by 3150:
\[ x = \frac{25200}{3150} \]

### Step 8: Simplify the division
Calculating \( \frac{25200}{3150} \):
\[ x = 8 \]

### Conclusion
The value of \( ? \) is \( 8 \).

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