If `(4)/(7)k=36`, then `(3)/(7)k=`

Options

A. `21`
B. `27`
C. `32`
D. `35`

Answer

To solve the equation \(\frac{4}{7}k = 36\) and find the value of \(\frac{3}{7}k\), we can follow these steps:

### Step 1: Solve for \(k\)
We start with the equation:
\[ \frac{4}{7}k = 36 \]
To isolate \(k\), we can multiply both sides of the equation by the reciprocal of \(\frac{4}{7}\), which is \(\frac{7}{4}\):
\[ k = 36 \times \frac{7}{4} \]

### Step 2: Calculate \(k\)
Now, we perform the multiplication:
\[ k = 36 \times \frac{7}{4} = \frac{36 \times 7}{4} \]
Calculating \(36 \times 7\):
\[ 36 \times 7 = 252 \]
Now, divide by 4:
\[ k = \frac{252}{4} = 63 \]

### Step 3: Find \(\frac{3}{7}k\)
Now that we have \(k = 63\), we can find \(\frac{3}{7}k\):
\[ \frac{3}{7}k = \frac{3}{7} \times 63 \]

### Step 4: Calculate \(\frac{3}{7}k\)
Now, we perform the multiplication:
\[ \frac{3}{7} \times 63 = \frac{3 \times 63}{7} \]
Calculating \(3 \times 63\):
\[ 3 \times 63 = 189 \]
Now, divide by 7:
\[ \frac{189}{7} = 27 \]

### Final Answer
Thus, the value of \(\frac{3}{7}k\) is:
\[ \frac{3}{7}k = 27 \]

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