If ` x = 3t , y = (1)/(2) ( t + 1)` , then the value of t for which x = 2y is

Options

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

Answer

To solve the problem, we need to find the value of \( t \) for which \( x = 2y \) given the equations \( x = 3t \) and \( y = \frac{1}{2}(t + 1) \).

### Step-by-step Solution:

1. **Write down the given equations**:
\[ x = 3t \]
\[ y = \frac{1}{2}(t + 1) \]

2. **Substitute \( y \) in the equation \( x = 2y \)**:
We need to express \( 2y \):
\[ 2y = 2 \cdot \frac{1}{2}(t + 1) = t + 1 \]

3. **Set up the equation \( x = 2y \)**:
Now we can equate \( x \) and \( 2y \):
\[ 3t = t + 1 \]

4. **Rearrange the equation to isolate \( t \)**:
Subtract \( t \) from both sides:
\[ 3t - t = 1 \]
This simplifies to:
\[ 2t = 1 \]

5. **Solve for \( t \)**:
Divide both sides by 2:
\[ t = \frac{1}{2} \]

### Final Answer:
The value of \( t \) for which \( x = 2y \) is:
\[ \boxed{\frac{1}{2}} \]