If `(3)/(7)` of 64% of `(x)/(21)` is 1280, then the value of x is ________.

Options

A. 98000
B. 64000
C. 8000
D. 4900

Answer

To solve the equation given in the problem, we need to follow these steps:

### Step 1: Set up the equation
We start with the equation given in the problem:
\[ \frac{3}{7} \times 64\% \times \frac{x}{21} = 1280 \]

### Step 2: Convert 64% to a fraction
We know that 64% can be expressed as a fraction:
\[ 64\% = \frac{64}{100} = \frac{16}{25} \]

### Step 3: Substitute the fraction into the equation
Now we substitute \(64\%\) in the equation:
\[ \frac{3}{7} \times \frac{16}{25} \times \frac{x}{21} = 1280 \]

### Step 4: Simplify the left side
Now we can simplify the left side of the equation:
\[ \frac{3 \times 16 \times x}{7 \times 25 \times 21} = 1280 \]

Calculating the denominator:
\[ 7 \times 25 \times 21 = 3675 \]
Thus, the equation becomes:
\[ \frac{48x}{3675} = 1280 \]

### Step 5: Cross-multiply to eliminate the fraction
To eliminate the fraction, we can cross-multiply:
\[ 48x = 1280 \times 3675 \]

### Step 6: Calculate \(1280 \times 3675\)
Now we calculate:
\[ 1280 \times 3675 = 4704000 \]
So, we have:
\[ 48x = 4704000 \]

### Step 7: Solve for \(x\)
Now divide both sides by 48 to find \(x\):
\[ x = \frac{4704000}{48} \]

### Step 8: Calculate \(x\)
Now, we perform the division:
\[ x = 98000 \]

Thus, the value of \(x\) is:
\[ \boxed{98000} \]