`15% "of" 84xx24% "of" 85=?`

Options

A. 424.2
B. 488.4
C. 482.8
D. 428.4

Explanation

To solve the problem \(15\% \text{ of } 84 \times 24\% \text{ of } 85 = ?\), we can break it down step by step.

### Step 1: Convert percentages to fractions
We start by converting the percentages into fractions:
- \(15\% = \frac{15}{100}\)
- \(24\% = \frac{24}{100}\)

### Step 2: Write the expression
Now we can rewrite the expression as:
\[ x = \left(\frac{15}{100} \times 84\right) \times \left(\frac{24}{100} \times 85\right) \]

### Step 3: Simplify the fractions
We can simplify the fractions:
- For \( \frac{15}{100} \), we can divide both the numerator and the denominator by 5:
\[ \frac{15 \div 5}{100 \div 5} = \frac{3}{20} \]
- For \( \frac{24}{100} \), we can divide both the numerator and the denominator by 4:
\[ \frac{24 \div 4}{100 \div 4} = \frac{6}{25} \]

### Step 4: Substitute back into the expression
Substituting back, we have:
\[ x = \left(\frac{3}{20} \times 84\right) \times \left(\frac{6}{25} \times 85\right) \]

### Step 5: Calculate each part
Now we calculate each part:
1. Calculate \( \frac{3}{20} \times 84 \):
\[ \frac{3 \times 84}{20} = \frac{252}{20} = 12.6 \]
2. Calculate \( \frac{6}{25} \times 85 \):
\[ \frac{6 \times 85}{25} = \frac{510}{25} = 20.4 \]

### Step 6: Multiply the results
Now we multiply the results from the two calculations:
\[ x = 12.6 \times 20.4 \]

### Step 7: Perform the multiplication
Calculating \( 12.6 \times 20.4 \):
\[ 12.6 \times 20.4 = 256.64 \]

### Final Answer
Thus, the final answer is:
\[ x = 256.64 \]

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