If the average (arithmetic mean) of k and `k+7` is b and if the average of k and `k-11` is c, what is the sum of b and c?

Options

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

Answer

To solve the problem, we need to find the sum of the averages \( b \) and \( c \) of two pairs of numbers involving \( k \).

### Step 1: Calculate the average \( b \)
The average of \( k \) and \( k + 7 \) is given by:
\[ b = \frac{k + (k + 7)}{2} \]
Simplifying this:
\[ b = \frac{2k + 7}{2} \]

### Step 2: Calculate the average \( c \)
The average of \( k \) and \( k - 11 \) is given by:
\[ c = \frac{k + (k - 11)}{2} \]
Simplifying this:
\[ c = \frac{2k - 11}{2} \]

### Step 3: Find the sum of \( b \) and \( c \)
Now we need to find \( b + c \):
\[ b + c = \frac{2k + 7}{2} + \frac{2k - 11}{2} \]
Since both fractions have the same denominator, we can combine them:
\[ b + c = \frac{(2k + 7) + (2k - 11)}{2} \]
Simplifying the numerator:
\[ b + c = \frac{2k + 2k + 7 - 11}{2} = \frac{4k - 4}{2} \]
Now, simplifying further:
\[ b + c = 2k - 2 \]

### Final Answer
The sum of \( b \) and \( c \) is:
\[ \boxed{2k - 2} \]