If `a-b=4, b-6=c, c-2=d, and a+d=4`,what is the value of a?

Options

A. `4`
B. `8`
C. `16`
D. It cannot be determined from the information given.

Answer

To solve the problem step by step, we will start by writing down the given equations and then manipulate them to find the value of \( a \).

### Step 1: Write down the equations
We have the following equations based on the problem statement:
1. \( a - b = 4 \) (Equation 1)
2. \( b - 6 = c \) (Equation 2)
3. \( c - 2 = d \) (Equation 3)
4. \( a + d = 4 \) (Equation 4)

### Step 2: Rewrite the equations
We can rearrange the equations to express \( b \), \( c \), and \( d \) in terms of \( a \):
- From Equation 1: \( b = a - 4 \)
- From Equation 2: \( c = b - 6 = (a - 4) - 6 = a - 10 \)
- From Equation 3: \( d = c - 2 = (a - 10) - 2 = a - 12 \)

### Step 3: Substitute \( d \) in Equation 4
Now we substitute \( d \) from our expression into Equation 4:
\[ a + d = 4 \]
Substituting for \( d \):
\[ a + (a - 12) = 4 \]
This simplifies to:
\[ 2a - 12 = 4 \]

### Step 4: Solve for \( a \)
Now, we solve for \( a \):
\[ 2a = 4 + 12 \]
\[ 2a = 16 \]
\[ a = \frac{16}{2} = 8 \]

### Final Answer
Thus, the value of \( a \) is \( 8 \).

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