If `(4)/(7)` of 49% of x = 21, then the value of x is ____.

Options

A. 125
B. 98
C. 84
D. 75

Explanation

To solve the equation \(\frac{4}{7}\) of 49% of \(x = 21\), we can follow these steps:

### Step 1: Convert the percentage to a fraction
We know that 49% can be expressed as a fraction:
\[ 49\% = \frac{49}{100} \]

### Step 2: Set up the equation
Now, we can rewrite the equation using the fraction for 49%:
\[ \frac{4}{7} \times \frac{49}{100} \times x = 21 \]

### Step 3: Simplify the left side
Multiply the fractions:
\[ \frac{4 \times 49}{7 \times 100} \times x = 21 \]
Calculating \(4 \times 49\):
\[ 4 \times 49 = 196 \]
Now we have:
\[ \frac{196}{700} \times x = 21 \]

### Step 4: Simplify the fraction
Now, simplify \(\frac{196}{700}\):
\[ \frac{196 \div 28}{700 \div 28} = \frac{7}{25} \]
So, the equation becomes:
\[ \frac{7}{25} \times x = 21 \]

### Step 5: Solve for \(x\)
To isolate \(x\), multiply both sides by the reciprocal of \(\frac{7}{25}\):
\[ x = 21 \times \frac{25}{7} \]

### Step 6: Calculate \(x\)
Now calculate:
\[ x = 21 \times \frac{25}{7} = 21 \div 7 \times 25 = 3 \times 25 = 75 \]

Thus, the value of \(x\) is:
\[ \boxed{75} \]

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