The final value, v, in a four-digit lock code is determined by multiplying the second value by two, subtracting that expression from the first value, and dividing the resulting expression by half of the third value. The first value is f, the second value is 1, and the third value is t. What is the final value, v, in terms of f and t ?

Options

A. `(f-2)/(t )`
B. `(2f -4)/(t )`
C. `(t)/(2f -4)`
D. `(2t-4)/(f)`

Explanation

To find the final value \( v \) in terms of \( f \) and \( t \), we can follow these steps:

1. **Identify the values**:
- The first value is \( f \).
- The second value is \( 1 \).
- The third value is \( t \).

2. **Multiply the second value by 2**:
\[ 2 \times 1 = 2 \]

3. **Subtract this result from the first value**:
\[ f - 2 \]

4. **Divide the resulting expression by half of the third value**:
- Half of the third value \( t \) is \( \frac{t}{2} \).
- Therefore, we need to divide \( f - 2 \) by \( \frac{t}{2} \):
\[ v = \frac{f - 2}{\frac{t}{2}} \]

5. **Simplify the division**:
- Dividing by \( \frac{t}{2} \) is the same as multiplying by \( \frac{2}{t} \):
\[ v = (f - 2) \times \frac{2}{t} = \frac{2(f - 2)}{t} \]

6. **Distribute the 2**:
\[ v = \frac{2f - 4}{t} \]

Thus, the final value \( v \) in terms of \( f \) and \( t \) is:
\[ v = \frac{2f - 4}{t} \]