If `(x)/(y)=6, (y)/(w)=4, and x=36`, what is the value of w?

Options

A. `(1)/(2)`
B. `(3)/(2)`
C. `2`
D. `4`

Answer

To solve the problem step by step, we start with the equations given:

1. **Given Equations**:
- \(\frac{x}{y} = 6\)
- \(\frac{y}{w} = 4\)
- \(x = 36\)

2. **Substituting the value of \(x\)**:
Since we know \(x = 36\), we can substitute this value into the first equation:
\[ \frac{36}{y} = 6 \]

3. **Solving for \(y\)**:
To find \(y\), we can cross-multiply:
\[ 36 = 6y \]
Now, divide both sides by 6:
\[ y = \frac{36}{6} = 6 \]

4. **Substituting \(y\) into the second equation**:
Now that we have \(y = 6\), we can substitute this value into the second equation:
\[ \frac{6}{w} = 4 \]

5. **Solving for \(w\)**:
Again, we cross-multiply:
\[ 6 = 4w \]
Now, divide both sides by 4:
\[ w = \frac{6}{4} = \frac{3}{2} \]

6. **Final Answer**:
Therefore, the value of \(w\) is \(\frac{3}{2}\).